sbplib: +scheme/Elastic2dVariableAnisotropicIncompatible.m annotate

author	Martin Almquist <martin.almquist@it.uu.se>
date	Tue, 30 Apr 2024 13:33:39 +0200
parents
children	464e6f65c2c6

rev	line source
1345 14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	1 classdef Elastic2dVariableAnisotropicIncompatible < scheme.Scheme
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	2
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	3 % Discretizes the elastic wave equation:
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	4 % rho u_{i,tt} = dj C_{ijkl} dk u_j
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	5 % opSet should be cell array of opSets, one per dimension. This
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	6 % is useful if we have periodic BC in one direction.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	7 % Assumes fully compatible operators
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	8
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	9 properties
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	10 m % Number of points in each direction, possibly a vector
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	11 h % Grid spacing
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	12
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	13 grid
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	14 dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	15
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	16 order % Order of accuracy for the approximation
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	17
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	18 % Diagonal matrices for variable coefficients
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	19 RHO, RHOi, RHOi_kron % Density
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	20 C % Elastic stiffness tensor
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	21
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	22 D % Total operator
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	23 D1 % First derivatives
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	24 % D2 % Second derivatives
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	25
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	26 % Boundary operators in cell format, used for BC
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	27 T_w, T_e, T_s, T_n
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	28
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	29 % Traction operators
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	30 tau_w, tau_e, tau_s, tau_n % Return vector field
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	31 tau1_w, tau1_e, tau1_s, tau1_n % Return scalar field
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	32 tau2_w, tau2_e, tau2_s, tau2_n % Return scalar field
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	33
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	34 % Inner products
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	35 H, Hi, Hi_kron, H_1D
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	36
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	37 % Boundary inner products (for scalar field)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	38 H_w, H_e, H_s, H_n
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	39
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	40 % Boundary restriction operators
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	41 e_w, e_e, e_s, e_n % Act on vector field, return vector field at boundary
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	42 e1_w, e1_e, e1_s, e1_n % Act on vector field, return scalar field at boundary
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	43 e2_w, e2_e, e2_s, e2_n % Act on vector field, return scalar field at boundary
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	44 e_scalar_w, e_scalar_e, e_scalar_s, e_scalar_n; % Act on scalar field, return scalar field
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	45
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	46 % E{i}^T picks out component i
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	47 E
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	48
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	49 % Borrowing constants of the form gamma*h, where gamma is a dimensionless constant.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	50 h11 % First entry in norm matrix
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	51 theta_R % Borrowing from R
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	52
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	53 nBP % Number of boundary points, related to borrowing.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	54 e_shifted_scalar_w, e_shifted_scalar_e, e_shifted_scalar_s, e_shifted_scalar_n; % Act on scalar field, return scalar field
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	55
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	56 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	57
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	58 methods
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	59
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	60 % The coefficients can either be function handles or grid functions
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	61 function obj = Elastic2dVariableAnisotropicIncompatible(g, order, rho, C, opSet, optFlag)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	62 default_arg('rho', @(x,y) 0*x+1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	63 default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	64 dim = 2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	65
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	66 C_default = cell(dim,dim,dim,dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	67 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	68 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	69 for k = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	70 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	71 C_default{i,j,k,l} = @(x,y) 0*x + 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	72 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	73 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	74 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	75 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	76 default_arg('C', C_default);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	77 assert(isa(g, 'grid.Cartesian'))
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	78
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	79 if isa(rho, 'function_handle')
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	80 rho = grid.evalOn(g, rho);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	81 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	82
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	83 C_mat = cell(dim,dim,dim,dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	84 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	85 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	86 for k = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	87 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	88 if isa(C{i,j,k,l}, 'function_handle')
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	89 C{i,j,k,l} = grid.evalOn(g, C{i,j,k,l});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	90 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	91 C_mat{i,j,k,l} = spdiag(C{i,j,k,l});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	92 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	93 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	94 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	95 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	96 obj.C = C_mat;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	97
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	98 m = g.size();
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	99 m_tot = g.N();
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	100 lim = g.lim;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	101 if isempty(lim)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	102 x = g.x;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	103 lim = cell(length(x),1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	104 for i = 1:length(x)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	105 lim{i} = {min(x{i}), max(x{i})};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	106 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	107 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	108
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	109 % 1D operators
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	110 ops = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	111 h = zeros(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	112 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	113 ops{i} = opSet{i}(m(i), lim{i}, order);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	114 h(i) = ops{i}.h;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	115 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	116
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	117 % Borrowing constants
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	118 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	119 obj.h11{i} = h(i)*ops{i}.borrowing.H11;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	120 obj.theta_R{i} = h(i)*ops{i}.borrowing.R.delta_D;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	121 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	122
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	123 switch order
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	124 case 2
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	125 width = 3;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	126 nBP = 2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	127 case 4
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	128 width = 5;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	129 nBP = 6;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	130 case 6
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	131 width = 7;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	132 nBP = 9;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	133 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	134
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	135 I = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	136 D1 = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	137 D2 = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	138 H = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	139 Hi = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	140 e_0 = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	141 e_m = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	142 d1_0 = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	143 d1_m = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	144
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	145 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	146 I{i} = speye(m(i));
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	147 D1{i} = ops{i}.D1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	148 D2{i} = ops{i}.D2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	149 H{i} = ops{i}.H;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	150 Hi{i} = ops{i}.HI;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	151 e_0{i} = ops{i}.e_l;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	152 e_m{i} = ops{i}.e_r;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	153 d1_0{i} = ops{i}.d1_l;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	154 d1_m{i} = ops{i}.d1_r;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	155 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	156
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	157 %====== Assemble full operators ========
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	158 I_dim = speye(dim, dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	159 RHO = spdiag(rho);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	160 obj.RHO = RHO;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	161 obj.RHOi = inv(RHO);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	162 obj.RHOi_kron = kron(obj.RHOi, I_dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	163
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	164 obj.D1 = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	165 D2_temp = cell(dim,dim,dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	166
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	167 % D1
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	168 obj.D1{1} = kron(D1{1},I{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	169 obj.D1{2} = kron(I{1},D1{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	170
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	171 % Boundary restriction operators
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	172 e_l = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	173 e_r = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	174 e_l{1} = kron(e_0{1}, I{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	175 e_l{2} = kron(I{1}, e_0{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	176 e_r{1} = kron(e_m{1}, I{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	177 e_r{2} = kron(I{1}, e_m{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	178
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	179 e_scalar_w = e_l{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	180 e_scalar_e = e_r{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	181 e_scalar_s = e_l{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	182 e_scalar_n = e_r{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	183
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	184 e_w = kron(e_scalar_w, I_dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	185 e_e = kron(e_scalar_e, I_dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	186 e_s = kron(e_scalar_s, I_dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	187 e_n = kron(e_scalar_n, I_dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	188
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	189 % Boundary restriction, shifted up to nBP-1 points
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	190 e_shifted_scalar_w = cell(nBP, 1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	191 e_shifted_scalar_e = cell(nBP, 1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	192 e_shifted_scalar_s = cell(nBP, 1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	193 e_shifted_scalar_n = cell(nBP, 1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	194 for i = 1:nBP-1
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	195 e_0_nBP = {0e_0{1}, 0e_0{2}};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	196 e_m_nBP = {0e_m{1}, 0e_m{2}};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	197 e_0_nBP{1}(i) = 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	198 e_0_nBP{2}(i) = 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	199 e_m_nBP{1}(end+1-i) = 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	200 e_m_nBP{2}(end+1-i) = 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	201 e_shifted_scalar_w{i} = kron(e_0_nBP{1}, I{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	202 e_shifted_scalar_s{i} = kron(I{1}, e_0_nBP{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	203 e_shifted_scalar_e{i} = kron(e_m_nBP{1}, I{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	204 e_shifted_scalar_n{i} = kron(I{1}, e_m_nBP{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	205 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	206
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	207 % Boundary derivatives
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	208 d1_l = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	209 d1_r = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	210 d1_l{1} = kron(d1_0{1}, I{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	211 d1_l{2} = kron(I{1}, d1_0{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	212 d1_r{1} = kron(d1_m{1}, I{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	213 d1_r{2} = kron(I{1}, d1_m{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	214
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	215 % E{i}^T picks out component i.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	216 E = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	217 I = speye(m_tot,m_tot);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	218 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	219 e = sparse(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	220 e(i) = 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	221 E{i} = kron(I,e);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	222 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	223 obj.E = E;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	224
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	225 e1_w = (e_scalar_w'*E{1}')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	226 e1_e = (e_scalar_e'*E{1}')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	227 e1_s = (e_scalar_s'*E{1}')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	228 e1_n = (e_scalar_n'*E{1}')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	229
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	230 e2_w = (e_scalar_w'*E{2}')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	231 e2_e = (e_scalar_e'*E{2}')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	232 e2_s = (e_scalar_s'*E{2}')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	233 e2_n = (e_scalar_n'*E{2}')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	234
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	235 % D2
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	236 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	237 for k = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	238 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	239 D2_temp{j,k,l} = spalloc(m_tot, m_tot, width*m_tot);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	240 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	241 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	242 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	243 ind = grid.funcToMatrix(g, 1:m_tot);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	244
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	245 k = 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	246 for r = 1:m(2)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	247 p = ind(:,r);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	248 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	249 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	250 coeff = C{k,j,k,l};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	251 D_kk = D2{1}(coeff(p));
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	252 D2_temp{j,k,l}(p,p) = D_kk;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	253 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	254 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	255 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	256
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	257 k = 2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	258 for r = 1:m(1)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	259 p = ind(r,:);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	260 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	261 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	262 coeff = C{k,j,k,l};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	263 D_kk = D2{2}(coeff(p));
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	264 D2_temp{j,k,l}(p,p) = D_kk;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	265 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	266 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	267 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	268
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	269 % Quadratures
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	270 obj.H = kron(H{1},H{2});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	271 obj.Hi = inv(obj.H);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	272 obj.H_w = H{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	273 obj.H_e = H{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	274 obj.H_s = H{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	275 obj.H_n = H{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	276 obj.H_1D = {H{1}, H{2}};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	277
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	278 % Differentiation matrix D (without SAT)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	279 D1 = obj.D1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	280 D = sparse(dimm_tot,dimm_tot);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	281 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	282 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	283 for k = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	284 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	285 if i == k
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	286 D = D + E{j}D2_temp{j,k,l}E{l}';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	287 D2_temp{j,k,l} = [];
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	288 else
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	289 D = D + E{j}(D1{i})C_mat{i,j,k,l}D1{k}E{l}';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	290 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	291 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	292 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	293 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	294 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	295 clear D2_temp;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	296 D = obj.RHOi_kron*D;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	297 obj.D = D;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	298 clear D;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	299 %=========================================%'
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	300
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	301 % Numerical traction operators for BC.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	302 %
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	303 % Formula at boundary j: % tau^{j}_i = sum_l T^{j}_{il} u_l
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	304 %
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	305 T_l = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	306 T_r = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	307 tau_l = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	308 tau_r = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	309
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	310 D1 = obj.D1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	311
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	312 d = @kroneckerDelta; % Kronecker delta
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	313 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	314
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	315 % Boundary j
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	316 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	317 T_l{j} = cell(dim,dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	318 T_r{j} = cell(dim,dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	319 tau_l{j} = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	320 tau_r{j} = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	321
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	322 [~, n_l] = size(e_l{j});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	323 [~, n_r] = size(e_r{j});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	324
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	325 % Traction component i
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	326 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	327 tau_l{j}{i} = sparse(dim*m_tot, n_l);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	328 tau_r{j}{i} = sparse(dim*m_tot, n_r);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	329
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	330 % Displacement component l
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	331 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	332 T_l{j}{i,l} = sparse(m_tot, n_l);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	333 T_r{j}{i,l} = sparse(m_tot, n_r);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	334
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	335 % Derivative direction k
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	336 for k = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	337 T_l{j}{i,l} = T_l{j}{i,l} ...
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	338 - d(j,k)(e_l{j}'C_mat{j,i,k,l}e_l{j}d1_l{k}')'...
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	339 - db(j,k)(e_l{j}'C_mat{j,i,k,l}*D1{k})';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	340 T_r{j}{i,l} = T_r{j}{i,l} ...
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	341 + d(j,k)(e_r{j}'C_mat{j,i,k,l}e_r{j}d1_r{k}')'...
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	342 + db(j,k)(e_r{j}'C_mat{j,i,k,l}*D1{k})';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	343 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	344 tau_l{j}{i} = tau_l{j}{i} + (T_l{j}{i,l}'*E{l}')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	345 tau_r{j}{i} = tau_r{j}{i} + (T_r{j}{i,l}'*E{l}')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	346 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	347 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	348 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	349
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	350 % Traction tensors, T_ij
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	351 obj.T_w = T_l{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	352 obj.T_e = T_r{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	353 obj.T_s = T_l{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	354 obj.T_n = T_r{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	355
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	356 % Restriction operators
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	357 obj.e_w = e_w;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	358 obj.e_e = e_e;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	359 obj.e_s = e_s;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	360 obj.e_n = e_n;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	361
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	362 obj.e1_w = e1_w;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	363 obj.e1_e = e1_e;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	364 obj.e1_s = e1_s;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	365 obj.e1_n = e1_n;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	366
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	367 obj.e2_w = e2_w;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	368 obj.e2_e = e2_e;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	369 obj.e2_s = e2_s;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	370 obj.e2_n = e2_n;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	371
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	372 obj.e_scalar_w = e_scalar_w;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	373 obj.e_scalar_e = e_scalar_e;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	374 obj.e_scalar_s = e_scalar_s;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	375 obj.e_scalar_n = e_scalar_n;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	376
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	377
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	378 obj.e_shifted_scalar_w = e_shifted_scalar_w;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	379 obj.e_shifted_scalar_e = e_shifted_scalar_e;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	380 obj.e_shifted_scalar_s = e_shifted_scalar_s;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	381 obj.e_shifted_scalar_n = e_shifted_scalar_n;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	382
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	383 % First component of traction
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	384 obj.tau1_w = tau_l{1}{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	385 obj.tau1_e = tau_r{1}{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	386 obj.tau1_s = tau_l{2}{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	387 obj.tau1_n = tau_r{2}{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	388
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	389 % Second component of traction
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	390 obj.tau2_w = tau_l{1}{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	391 obj.tau2_e = tau_r{1}{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	392 obj.tau2_s = tau_l{2}{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	393 obj.tau2_n = tau_r{2}{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	394
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	395 % Traction vectors
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	396 obj.tau_w = (e_w'e1_wobj.tau1_w')' + (e_w'e2_wobj.tau2_w')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	397 obj.tau_e = (e_e'e1_eobj.tau1_e')' + (e_e'e2_eobj.tau2_e')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	398 obj.tau_s = (e_s'e1_sobj.tau1_s')' + (e_s'e2_sobj.tau2_s')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	399 obj.tau_n = (e_n'e1_nobj.tau1_n')' + (e_n'e2_nobj.tau2_n')';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	400
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	401 % Kroneckered norms and coefficients
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	402 obj.Hi_kron = kron(obj.Hi, I_dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	403
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	404 % Misc.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	405 obj.m = m;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	406 obj.h = h;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	407 obj.order = order;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	408 obj.grid = g;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	409 obj.dim = dim;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	410 obj.nBP = nBP;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	411
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	412 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	413
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	414
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	415 % Closure functions return the operators applied to the own domain to close the boundary
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	416 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	417 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	418 % bc is a cell array of component and bc type, e.g. {1, 'd'} for Dirichlet condition
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	419 % on the first component. Can also be e.g.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	420 % {'normal', 'd'} or {'tangential', 't'} for conditions on
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	421 % tangential/normal component.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	422 % data is a function returning the data that should be applied at the boundary.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	423 % neighbour_scheme is an instance of Scheme that should be interfaced to.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	424 % neighbour_boundary is a string specifying which boundary to interface to.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	425
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	426 % For displacement bc:
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	427 % bc = {comp, 'd', dComps},
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	428 % where
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	429 % dComps = vector of components with displacement BC. Default: 1:dim.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	430 % In this way, we can specify one BC at a time even though the SATs depend on all BC.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	431 function [closure, penalty] = boundary_condition(obj, boundary, bc, tuning)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	432 default_arg('tuning', 1.0);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	433
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	434 assert( iscell(bc), 'The BC type must be a 2x1 or 3x1 cell array' );
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	435 comp = bc{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	436 type = bc{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	437 if ischar(comp)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	438 comp = obj.getComponent(comp, boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	439 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	440
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	441 e = obj.getBoundaryOperatorForScalarField('e', boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	442 e_sh = obj.getBoundaryOperatorForScalarField('e_shifted', boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	443 tau = obj.getBoundaryOperator(['tau' num2str(comp)], boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	444 T = obj.getBoundaryTractionOperator(boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	445 [h11, th_R] = obj.getBorrowing(boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	446 H_gamma = obj.getBoundaryQuadratureForScalarField(boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	447 nu = obj.getNormal(boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	448
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	449 E = obj.E;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	450 Hi = obj.Hi;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	451 RHOi = obj.RHOi;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	452 C = obj.C;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	453
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	454 dim = obj.dim;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	455 m_tot = obj.grid.N();
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	456
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	457 % Preallocate
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	458 [~, col] = size(tau);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	459 closure = sparse(dimm_tot, dimm_tot);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	460 penalty = sparse(dim*m_tot, col);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	461
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	462 j = comp;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	463 switch type
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	464
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	465 % Dirichlet boundary condition
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	466 case {'D','d','dirichlet','Dirichlet','displacement','Displacement'}
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	467
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	468 if numel(bc) >= 3
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	469 dComps = bc{3};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	470 else
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	471 dComps = 1:dim;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	472 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	473
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	474 % Loops over components that Dirichlet penalties end up on
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	475 % Y: symmetrizing part of penalty
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	476 % Z: symmetric part of penalty
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	477 % X = Y + Z.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	478
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	479 % Nonsymmetric part goes on all components to
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	480 % yield traction in discrete energy rate
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	481 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	482 Y = T{j,i}';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	483 X = e*Y;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	484 closure = closure + E{i}RHOiHiX'eH_gamma(e'*E{j}' );
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	485 penalty = penalty - E{i}RHOiHiX'e*H_gamma;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	486 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	487
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	488 % Symmetric part only required on components with displacement BC.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	489 % (Otherwise it's not symmetric.)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	490
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	491 % 1. Compute beta such that C_bJbL_boundary - \beta*C_bJbL_i >= 0, i = 0, 1, ..., nBP.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	492 [~, N] = size(e);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	493 beta_vec = ones(N, 1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	494 b = obj.getComponent('normal', boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	495 C_boundary = cell(dim, dim, dim, dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	496 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	497 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	498 for k = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	499 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	500 C_boundary{i,j,k,l} = e'C{i,j,k,l}e ;

1345

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

1 classdef Elastic2dVariableAnisotropicIncompatible < scheme.Scheme

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

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diff changeset

2

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

3 % Discretizes the elastic wave equation:

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

4 % rho u_{i,tt} = dj C_{ijkl} dk u_j

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

5 % opSet should be cell array of opSets, one per dimension. This

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

6 % is useful if we have periodic BC in one direction.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

7 % Assumes fully compatible operators

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

8

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

9 properties

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

10 m % Number of points in each direction, possibly a vector

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

11 h % Grid spacing

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

12

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

13 grid

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

14 dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

15

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

16 order % Order of accuracy for the approximation

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

17

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

18 % Diagonal matrices for variable coefficients

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

19 RHO, RHOi, RHOi_kron % Density

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

20 C % Elastic stiffness tensor

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

21

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

22 D % Total operator

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

23 D1 % First derivatives

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

24 % D2 % Second derivatives

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

25

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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diff changeset

26 % Boundary operators in cell format, used for BC

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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diff changeset

27 T_w, T_e, T_s, T_n

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

28

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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diff changeset

29 % Traction operators

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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diff changeset

30 tau_w, tau_e, tau_s, tau_n % Return vector field

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

31 tau1_w, tau1_e, tau1_s, tau1_n % Return scalar field

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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diff changeset

32 tau2_w, tau2_e, tau2_s, tau2_n % Return scalar field

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

33

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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diff changeset

34 % Inner products

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

35 H, Hi, Hi_kron, H_1D

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

36

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

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diff changeset

37 % Boundary inner products (for scalar field)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

38 H_w, H_e, H_s, H_n

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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diff changeset

39

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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diff changeset

40 % Boundary restriction operators

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

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diff changeset

41 e_w, e_e, e_s, e_n % Act on vector field, return vector field at boundary

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

42 e1_w, e1_e, e1_s, e1_n % Act on vector field, return scalar field at boundary

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

43 e2_w, e2_e, e2_s, e2_n % Act on vector field, return scalar field at boundary

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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diff changeset

44 e_scalar_w, e_scalar_e, e_scalar_s, e_scalar_n; % Act on scalar field, return scalar field

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

45

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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diff changeset

46 % E{i}^T picks out component i

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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diff changeset

47 E

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

48

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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parents:

diff changeset

49 % Borrowing constants of the form gamma*h, where gamma is a dimensionless constant.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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diff changeset

50 h11 % First entry in norm matrix

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

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diff changeset

51 theta_R % Borrowing from R

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

52

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

53 nBP % Number of boundary points, related to borrowing.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

54 e_shifted_scalar_w, e_shifted_scalar_e, e_shifted_scalar_s, e_shifted_scalar_n; % Act on scalar field, return scalar field

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

55

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

56 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

57

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

58 methods

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

59

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

60 % The coefficients can either be function handles or grid functions

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

61 function obj = Elastic2dVariableAnisotropicIncompatible(g, order, rho, C, opSet, optFlag)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

62 default_arg('rho', @(x,y) 0*x+1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

63 default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

64 dim = 2;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

65

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

66 C_default = cell(dim,dim,dim,dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

67 for i = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

68 for j = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

69 for k = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

70 for l = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

71 C_default{i,j,k,l} = @(x,y) 0*x + 1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

72 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

73 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

74 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

75 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

76 default_arg('C', C_default);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

77 assert(isa(g, 'grid.Cartesian'))

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

78

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

79 if isa(rho, 'function_handle')

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

80 rho = grid.evalOn(g, rho);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

81 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

82

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

83 C_mat = cell(dim,dim,dim,dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

84 for i = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

85 for j = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

86 for k = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

87 for l = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

88 if isa(C{i,j,k,l}, 'function_handle')

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

89 C{i,j,k,l} = grid.evalOn(g, C{i,j,k,l});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

90 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

91 C_mat{i,j,k,l} = spdiag(C{i,j,k,l});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

92 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

93 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

94 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

95 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

96 obj.C = C_mat;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

97

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

98 m = g.size();

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

99 m_tot = g.N();

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

100 lim = g.lim;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

101 if isempty(lim)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

102 x = g.x;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

103 lim = cell(length(x),1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

104 for i = 1:length(x)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

105 lim{i} = {min(x{i}), max(x{i})};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

106 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

107 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

108

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

109 % 1D operators

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

110 ops = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

111 h = zeros(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

112 for i = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

113 ops{i} = opSet{i}(m(i), lim{i}, order);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

114 h(i) = ops{i}.h;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

115 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

116

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

117 % Borrowing constants

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

118 for i = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

119 obj.h11{i} = h(i)*ops{i}.borrowing.H11;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

120 obj.theta_R{i} = h(i)*ops{i}.borrowing.R.delta_D;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

121 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

122

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

123 switch order

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

124 case 2

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

125 width = 3;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

126 nBP = 2;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

127 case 4

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

128 width = 5;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

129 nBP = 6;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

130 case 6

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

131 width = 7;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

132 nBP = 9;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

133 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

134

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

135 I = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

136 D1 = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

137 D2 = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

138 H = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

139 Hi = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

140 e_0 = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

141 e_m = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

142 d1_0 = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

143 d1_m = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

144

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

145 for i = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

146 I{i} = speye(m(i));

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

147 D1{i} = ops{i}.D1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

148 D2{i} = ops{i}.D2;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

149 H{i} = ops{i}.H;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

150 Hi{i} = ops{i}.HI;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

151 e_0{i} = ops{i}.e_l;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

152 e_m{i} = ops{i}.e_r;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

153 d1_0{i} = ops{i}.d1_l;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

154 d1_m{i} = ops{i}.d1_r;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

155 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

156

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

157 %====== Assemble full operators ========

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

158 I_dim = speye(dim, dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

159 RHO = spdiag(rho);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

160 obj.RHO = RHO;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

161 obj.RHOi = inv(RHO);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

162 obj.RHOi_kron = kron(obj.RHOi, I_dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

163

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

164 obj.D1 = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

165 D2_temp = cell(dim,dim,dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

166

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

167 % D1

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

168 obj.D1{1} = kron(D1{1},I{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

169 obj.D1{2} = kron(I{1},D1{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

170

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

171 % Boundary restriction operators

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

172 e_l = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

173 e_r = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

174 e_l{1} = kron(e_0{1}, I{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

175 e_l{2} = kron(I{1}, e_0{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

176 e_r{1} = kron(e_m{1}, I{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

177 e_r{2} = kron(I{1}, e_m{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

178

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

179 e_scalar_w = e_l{1};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

180 e_scalar_e = e_r{1};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

181 e_scalar_s = e_l{2};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

182 e_scalar_n = e_r{2};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

183

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

184 e_w = kron(e_scalar_w, I_dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

185 e_e = kron(e_scalar_e, I_dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

186 e_s = kron(e_scalar_s, I_dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

187 e_n = kron(e_scalar_n, I_dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

188

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

189 % Boundary restriction, shifted up to nBP-1 points

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

190 e_shifted_scalar_w = cell(nBP, 1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

191 e_shifted_scalar_e = cell(nBP, 1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

192 e_shifted_scalar_s = cell(nBP, 1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

193 e_shifted_scalar_n = cell(nBP, 1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

194 for i = 1:nBP-1

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

195 e_0_nBP = {0*e_0{1}, 0*e_0{2}};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

196 e_m_nBP = {0*e_m{1}, 0*e_m{2}};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

197 e_0_nBP{1}(i) = 1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

198 e_0_nBP{2}(i) = 1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

199 e_m_nBP{1}(end+1-i) = 1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

200 e_m_nBP{2}(end+1-i) = 1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

201 e_shifted_scalar_w{i} = kron(e_0_nBP{1}, I{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

202 e_shifted_scalar_s{i} = kron(I{1}, e_0_nBP{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

203 e_shifted_scalar_e{i} = kron(e_m_nBP{1}, I{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

204 e_shifted_scalar_n{i} = kron(I{1}, e_m_nBP{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

205 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

206

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

207 % Boundary derivatives

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

208 d1_l = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

209 d1_r = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

210 d1_l{1} = kron(d1_0{1}, I{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

211 d1_l{2} = kron(I{1}, d1_0{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

212 d1_r{1} = kron(d1_m{1}, I{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

213 d1_r{2} = kron(I{1}, d1_m{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

214

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

215 % E{i}^T picks out component i.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

216 E = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

217 I = speye(m_tot,m_tot);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

218 for i = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

219 e = sparse(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

220 e(i) = 1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

221 E{i} = kron(I,e);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

222 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

223 obj.E = E;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

224

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

225 e1_w = (e_scalar_w'*E{1}')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

226 e1_e = (e_scalar_e'*E{1}')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

227 e1_s = (e_scalar_s'*E{1}')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

228 e1_n = (e_scalar_n'*E{1}')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

229

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

230 e2_w = (e_scalar_w'*E{2}')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

231 e2_e = (e_scalar_e'*E{2}')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

232 e2_s = (e_scalar_s'*E{2}')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

233 e2_n = (e_scalar_n'*E{2}')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

234

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

235 % D2

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

236 for j = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

237 for k = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

238 for l = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

239 D2_temp{j,k,l} = spalloc(m_tot, m_tot, width*m_tot);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

240 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

241 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

242 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

243 ind = grid.funcToMatrix(g, 1:m_tot);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

244

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

245 k = 1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

246 for r = 1:m(2)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

247 p = ind(:,r);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

248 for j = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

249 for l = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

250 coeff = C{k,j,k,l};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

251 D_kk = D2{1}(coeff(p));

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

252 D2_temp{j,k,l}(p,p) = D_kk;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

253 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

254 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

255 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

256

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

257 k = 2;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

258 for r = 1:m(1)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

259 p = ind(r,:);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

260 for j = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

261 for l = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

262 coeff = C{k,j,k,l};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

263 D_kk = D2{2}(coeff(p));

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

264 D2_temp{j,k,l}(p,p) = D_kk;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

265 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

266 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

267 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

268

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

269 % Quadratures

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

270 obj.H = kron(H{1},H{2});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

271 obj.Hi = inv(obj.H);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

272 obj.H_w = H{2};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

273 obj.H_e = H{2};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

274 obj.H_s = H{1};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

275 obj.H_n = H{1};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

276 obj.H_1D = {H{1}, H{2}};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

277

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

278 % Differentiation matrix D (without SAT)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

279 D1 = obj.D1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

280 D = sparse(dim*m_tot,dim*m_tot);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

281 for i = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

282 for j = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

283 for k = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

284 for l = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

285 if i == k

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

286 D = D + E{j}*D2_temp{j,k,l}*E{l}';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

287 D2_temp{j,k,l} = [];

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

288 else

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

289 D = D + E{j}*(D1{i})*C_mat{i,j,k,l}*D1{k}*E{l}';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

290 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

291 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

292 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

293 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

294 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

295 clear D2_temp;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

296 D = obj.RHOi_kron*D;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

297 obj.D = D;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

298 clear D;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

299 %=========================================%'

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

300

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

301 % Numerical traction operators for BC.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

302 %

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

303 % Formula at boundary j: % tau^{j}_i = sum_l T^{j}_{il} u_l

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

304 %

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

305 T_l = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

306 T_r = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

307 tau_l = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

308 tau_r = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

309

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

310 D1 = obj.D1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

311

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

312 d = @kroneckerDelta; % Kronecker delta

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

313 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

314

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

315 % Boundary j

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

316 for j = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

317 T_l{j} = cell(dim,dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

318 T_r{j} = cell(dim,dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

319 tau_l{j} = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

320 tau_r{j} = cell(dim,1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

321

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

322 [~, n_l] = size(e_l{j});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

323 [~, n_r] = size(e_r{j});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

324

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

325 % Traction component i

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

326 for i = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

327 tau_l{j}{i} = sparse(dim*m_tot, n_l);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

328 tau_r{j}{i} = sparse(dim*m_tot, n_r);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

329

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

330 % Displacement component l

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

331 for l = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

332 T_l{j}{i,l} = sparse(m_tot, n_l);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

333 T_r{j}{i,l} = sparse(m_tot, n_r);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

334

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

335 % Derivative direction k

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

336 for k = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

337 T_l{j}{i,l} = T_l{j}{i,l} ...

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

338 - d(j,k)*(e_l{j}'*C_mat{j,i,k,l}*e_l{j}*d1_l{k}')'...

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

339 - db(j,k)*(e_l{j}'*C_mat{j,i,k,l}*D1{k})';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

340 T_r{j}{i,l} = T_r{j}{i,l} ...

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

341 + d(j,k)*(e_r{j}'*C_mat{j,i,k,l}*e_r{j}*d1_r{k}')'...

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

342 + db(j,k)*(e_r{j}'*C_mat{j,i,k,l}*D1{k})';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

343 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

344 tau_l{j}{i} = tau_l{j}{i} + (T_l{j}{i,l}'*E{l}')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

345 tau_r{j}{i} = tau_r{j}{i} + (T_r{j}{i,l}'*E{l}')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

346 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

347 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

348 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

349

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

350 % Traction tensors, T_ij

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

351 obj.T_w = T_l{1};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

352 obj.T_e = T_r{1};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

353 obj.T_s = T_l{2};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

354 obj.T_n = T_r{2};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

355

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

356 % Restriction operators

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

357 obj.e_w = e_w;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

358 obj.e_e = e_e;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

359 obj.e_s = e_s;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

360 obj.e_n = e_n;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

361

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

362 obj.e1_w = e1_w;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

363 obj.e1_e = e1_e;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

364 obj.e1_s = e1_s;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

365 obj.e1_n = e1_n;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

366

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

367 obj.e2_w = e2_w;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

368 obj.e2_e = e2_e;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

369 obj.e2_s = e2_s;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

370 obj.e2_n = e2_n;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

371

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

372 obj.e_scalar_w = e_scalar_w;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

373 obj.e_scalar_e = e_scalar_e;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

374 obj.e_scalar_s = e_scalar_s;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

375 obj.e_scalar_n = e_scalar_n;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

376

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

377

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

378 obj.e_shifted_scalar_w = e_shifted_scalar_w;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

379 obj.e_shifted_scalar_e = e_shifted_scalar_e;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

380 obj.e_shifted_scalar_s = e_shifted_scalar_s;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

381 obj.e_shifted_scalar_n = e_shifted_scalar_n;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

382

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

383 % First component of traction

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

384 obj.tau1_w = tau_l{1}{1};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

385 obj.tau1_e = tau_r{1}{1};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

386 obj.tau1_s = tau_l{2}{1};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

387 obj.tau1_n = tau_r{2}{1};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

388

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

389 % Second component of traction

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

390 obj.tau2_w = tau_l{1}{2};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

391 obj.tau2_e = tau_r{1}{2};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

392 obj.tau2_s = tau_l{2}{2};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

393 obj.tau2_n = tau_r{2}{2};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

394

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

395 % Traction vectors

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

396 obj.tau_w = (e_w'*e1_w*obj.tau1_w')' + (e_w'*e2_w*obj.tau2_w')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

397 obj.tau_e = (e_e'*e1_e*obj.tau1_e')' + (e_e'*e2_e*obj.tau2_e')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

398 obj.tau_s = (e_s'*e1_s*obj.tau1_s')' + (e_s'*e2_s*obj.tau2_s')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

399 obj.tau_n = (e_n'*e1_n*obj.tau1_n')' + (e_n'*e2_n*obj.tau2_n')';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

400

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

401 % Kroneckered norms and coefficients

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

402 obj.Hi_kron = kron(obj.Hi, I_dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

403

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

404 % Misc.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

405 obj.m = m;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

406 obj.h = h;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

407 obj.order = order;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

408 obj.grid = g;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

409 obj.dim = dim;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

410 obj.nBP = nBP;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

411

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

412 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

413

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

414

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

415 % Closure functions return the operators applied to the own domain to close the boundary

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

416 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

417 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

418 % bc is a cell array of component and bc type, e.g. {1, 'd'} for Dirichlet condition

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

419 % on the first component. Can also be e.g.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

420 % {'normal', 'd'} or {'tangential', 't'} for conditions on

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

421 % tangential/normal component.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

422 % data is a function returning the data that should be applied at the boundary.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

423 % neighbour_scheme is an instance of Scheme that should be interfaced to.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

424 % neighbour_boundary is a string specifying which boundary to interface to.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

425

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

426 % For displacement bc:

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

427 % bc = {comp, 'd', dComps},

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

428 % where

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

429 % dComps = vector of components with displacement BC. Default: 1:dim.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

430 % In this way, we can specify one BC at a time even though the SATs depend on all BC.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

431 function [closure, penalty] = boundary_condition(obj, boundary, bc, tuning)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

432 default_arg('tuning', 1.0);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

433

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

434 assert( iscell(bc), 'The BC type must be a 2x1 or 3x1 cell array' );

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

435 comp = bc{1};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

436 type = bc{2};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

437 if ischar(comp)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

438 comp = obj.getComponent(comp, boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

439 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

440

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

441 e = obj.getBoundaryOperatorForScalarField('e', boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

442 e_sh = obj.getBoundaryOperatorForScalarField('e_shifted', boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

443 tau = obj.getBoundaryOperator(['tau' num2str(comp)], boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

444 T = obj.getBoundaryTractionOperator(boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

445 [h11, th_R] = obj.getBorrowing(boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

446 H_gamma = obj.getBoundaryQuadratureForScalarField(boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

447 nu = obj.getNormal(boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

448

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

449 E = obj.E;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

450 Hi = obj.Hi;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

451 RHOi = obj.RHOi;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

452 C = obj.C;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

453

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

454 dim = obj.dim;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

455 m_tot = obj.grid.N();

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

456

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

457 % Preallocate

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

458 [~, col] = size(tau);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

459 closure = sparse(dim*m_tot, dim*m_tot);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

460 penalty = sparse(dim*m_tot, col);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

461

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

462 j = comp;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

463 switch type

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

464

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

465 % Dirichlet boundary condition

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

466 case {'D','d','dirichlet','Dirichlet','displacement','Displacement'}

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

467

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

468 if numel(bc) >= 3

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

469 dComps = bc{3};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

470 else

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

471 dComps = 1:dim;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

472 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

473

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

474 % Loops over components that Dirichlet penalties end up on

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

475 % Y: symmetrizing part of penalty

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

476 % Z: symmetric part of penalty

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

477 % X = Y + Z.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

478

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

479 % Nonsymmetric part goes on all components to

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

480 % yield traction in discrete energy rate

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

481 for i = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

482 Y = T{j,i}';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

483 X = e*Y;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

484 closure = closure + E{i}*RHOi*Hi*X'*e*H_gamma*(e'*E{j}' );

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

485 penalty = penalty - E{i}*RHOi*Hi*X'*e*H_gamma;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

486 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

487

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

488 % Symmetric part only required on components with displacement BC.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

489 % (Otherwise it's not symmetric.)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

490

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

491 % 1. Compute beta such that C_bJbL_boundary - \beta*C_bJbL_i >= 0, i = 0, 1, ..., nBP.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

492 [~, N] = size(e);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

493 beta_vec = ones(N, 1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

494 b = obj.getComponent('normal', boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

495 C_boundary = cell(dim, dim, dim, dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

496 for i = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

497 for j = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

498 for k = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

499 for l = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

500 C_boundary{i,j,k,l} = e'*C{i,j,k,l}*e ;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

501 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

502 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

503 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

504 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

505

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

506 % Loop over shift inward from boundary

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

507 for m = 1:obj.nBP-1

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

508 C_shifted = cell(dim, dim, dim, dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

509 for i = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

510 for j = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

511 for k = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

512 for l = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

513 C_shifted{i,j,k,l} = e_sh{m}'*C{i,j,k,l}*e_sh{m};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

514 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

515 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

516 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

517 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

518

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

519 % Loop along boundary

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

520 for i = 1:N

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

521 C_boundary_mat = [C_boundary{b,1,b,1}(i,i), C_boundary{b,1,b,2}(i,i); ...

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

522 C_boundary{b,2,b,1}(i,i), C_boundary{b,2,b,2}(i,i)];

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

523

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

524 C_shifted_mat = [C_shifted{b,1,b,1}(i,i), C_shifted{b,1,b,2}(i,i); ...

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

525 C_shifted{b,2,b,1}(i,i), C_shifted{b,2,b,2}(i,i)];

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

526

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

527 beta = obj.computeBorrowingFromC(C_boundary_mat, C_shifted_mat);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

528 beta_vec(i) = min(beta_vec(i), beta);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

529 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

530 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

531 if min(beta_vec) < 1e-10

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

532 disp('WARNING! No borrowing from C seems to be possible.')

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

533 disp(['min(beta) = ' num2str(min(beta_vec))])

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

534 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

535 beta_inv = e*spdiag(1./beta_vec)*e';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

536

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

537 % Compensate at corners

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

538 corner_weight = ones(N, 1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

539 corner_weight(1) = 2;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

540 corner_weight(end) = 2;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

541 corner_weight = e*spdiag(corner_weight)*e';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

542

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

543

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

544 % 2. Build Z.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

545 j = comp;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

546 for i = dComps

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

547 Z = sparse(m_tot, m_tot);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

548 for l = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

549 for k = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

550 Z = Z + nu(l)*C{l,i,k,j}*nu(k);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

551 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

552 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

553 Z = -1.2*tuning*(corner_weight/h11 + beta_inv/th_R)*Z;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

554 X = Z;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

555 closure = closure + E{i}*RHOi*Hi*X'*e*H_gamma*(e'*E{j}' );

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

556 penalty = penalty - E{i}*RHOi*Hi*X'*e*H_gamma;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

557 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

558

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

559 % Free boundary condition

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

560 case {'F','f','Free','free','traction','Traction','t','T'}

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

561 closure = closure - E{j}*RHOi*Hi*e*H_gamma*tau';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

562 penalty = penalty + E{j}*RHOi*Hi*e*H_gamma;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

563

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

564 % Unknown boundary condition

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

565 otherwise

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

566 error('No such boundary condition: type = %s',type);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

567 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

568 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

569

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

570 % type Struct that specifies the interface coupling.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

571 % Fields:

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

572 % -- tuning: penalty strength, defaults to 1.0

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

573 % -- interpolation: type of interpolation, default 'none'

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

574 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

575

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

576 defaultType.tuning = 1.0;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

577 defaultType.interpolation = 'none';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

578 default_struct('type', defaultType);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

579

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

580 switch type.interpolation

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

581 case {'none', ''}

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

582 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

583 case {'op','OP'}

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

584 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

585 otherwise

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

586 error('Unknown type of interpolation: %s ', type.interpolation);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

587 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

588 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

589

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

590 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

591 tuning = type.tuning;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

592

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

593 % u denotes the solution in the own domain

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

594 % v denotes the solution in the neighbour domain

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

595

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

596 u = obj;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

597 v = neighbour_scheme;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

598

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

599 % Operators, u side

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

600 e_u = u.getBoundaryOperatorForScalarField('e', boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

601 tau_u = u.getBoundaryOperator('tau', boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

602 h11_u = u.getBorrowing(boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

603 nu_u = u.getNormal(boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

604

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

605 E_u = u.E;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

606 C_u = u.C;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

607 m_tot_u = u.grid.N();

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

608

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

609 % Operators, v side

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

610 e_v = v.getBoundaryOperatorForScalarField('e', neighbour_boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

611 tau_v = v.getBoundaryOperator('tau', neighbour_boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

612 h11_v = v.getBorrowing(neighbour_boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

613 nu_v = v.getNormal(neighbour_boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

614

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

615 E_v = v.E;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

616 C_v = v.C;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

617 m_tot_v = v.grid.N();

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

618

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

619 % Fix {'e', 's'}, {'w', 'n'}, and {'x','x'} couplings

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

620 flipFlag = false;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

621 e_v_flip = e_v;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

622 if (strcmp(boundary,'s') && strcmp(neighbour_boundary,'e')) || ...

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

623 (strcmp(boundary,'e') && strcmp(neighbour_boundary,'s')) || ...

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

624 (strcmp(boundary,'w') && strcmp(neighbour_boundary,'n')) || ...

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

625 (strcmp(boundary,'n') && strcmp(neighbour_boundary,'w')) || ...

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

626 (strcmp(boundary,'s') && strcmp(neighbour_boundary,'s')) || ...

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

627 (strcmp(boundary,'n') && strcmp(neighbour_boundary,'n')) || ...

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

628 (strcmp(boundary,'w') && strcmp(neighbour_boundary,'w')) || ...

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

629 (strcmp(boundary,'e') && strcmp(neighbour_boundary,'e'))

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

630

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

631 flipFlag = true;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

632 e_v_flip = fliplr(e_v);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

633

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

634 t1 = tau_v(:,1:2:end-1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

635 t2 = tau_v(:,2:2:end);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

636

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

637 t1 = fliplr(t1);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

638 t2 = fliplr(t2);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

639

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

640 tau_v(:,1:2:end-1) = t1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

641 tau_v(:,2:2:end) = t2;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

642 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

643

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

644 % Operators that are only required for own domain

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

645 Hi = u.Hi_kron;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

646 RHOi = u.RHOi_kron;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

647 e_kron = u.getBoundaryOperator('e', boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

648 T_u = u.getBoundaryTractionOperator(boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

649

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

650 % Shared operators

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

651 H_gamma = u.getBoundaryQuadratureForScalarField(boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

652 H_gamma_kron = u.getBoundaryQuadrature(boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

653 dim = u.dim;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

654

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

655 % Preallocate

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

656 [~, m_int] = size(H_gamma);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

657 closure = sparse(dim*m_tot_u, dim*m_tot_u);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

658 penalty = sparse(dim*m_tot_u, dim*m_tot_v);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

659

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

660 % ---- Continuity of displacement ------

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

661

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

662 % Y: symmetrizing part of penalty

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

663 % Z: symmetric part of penalty

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

664 % X = Y + Z.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

665

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

666 % Loop over components to couple across interface

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

667 for j = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

668

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

669 % Loop over components that penalties end up on

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

670 for i = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

671 Y = 1/2*T_u{j,i}';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

672 Z_u = sparse(m_int, m_int);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

673 Z_v = sparse(m_int, m_int);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

674 for l = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

675 for k = 1:dim

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

676 Z_u = Z_u + e_u'*nu_u(l)*C_u{l,i,k,j}*nu_u(k)*e_u;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

677 Z_v = Z_v + e_v'*nu_v(l)*C_v{l,i,k,j}*nu_v(k)*e_v;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

678 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

679 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

680

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

681 if flipFlag

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

682 Z_v = rot90(Z_v,2);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

683 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

684

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

685 Z = -tuning*dim*( 1/(4*h11_u)*Z_u + 1/(4*h11_v)*Z_v );

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

686 X = Y + Z*e_u';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

687 closure = closure + E_u{i}*X'*H_gamma*e_u'*E_u{j}';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

688 penalty = penalty - E_u{i}*X'*H_gamma*e_v_flip'*E_v{j}';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

689

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

690 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

691 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

692

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

693 % ---- Continuity of traction ------

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

694 closure = closure - 1/2*e_kron*H_gamma_kron*tau_u';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

695 penalty = penalty - 1/2*e_kron*H_gamma_kron*tau_v';

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

696

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

697 % ---- Multiply by inverse of density x quadraure ----

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

698 closure = RHOi*Hi*closure;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

699 penalty = RHOi*Hi*penalty;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

700

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

701 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

702

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

703 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

704 error('Non-conforming interfaces not implemented yet.');

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

705 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

706

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

707 % Computes the largest beta such that C_b - beta*C_s >= 0, using bisection.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

708 function beta = computeBorrowingFromC(obj, C_b, C_s)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

709 tol = 1e-8;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

710 beta_min = 0;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

711 beta_max = 1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

712 beta = 0.5;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

713 err = (beta_max - beta_min)/2;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

714 while err > tol

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

715 if min(eig(C_b - beta*C_s)) < -1e-14

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

716 % Tried to borrow too much. Reduce beta.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

717 beta_max = beta;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

718 beta = (beta_min + beta)/2;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

719 else

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

720 % Increase beta

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

721 beta_min = beta;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

722 beta = (beta_max + beta)/2;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

723 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

724 err = err/2;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

725 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

726 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

727

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

728 % Returns the component number that is the tangential/normal component

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

729 % at the specified boundary

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

730 function comp = getComponent(obj, comp_str, boundary)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

731 assertIsMember(comp_str, {'normal', 'tangential'});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

732 assertIsMember(boundary, {'w', 'e', 's', 'n'});

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

733

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

734 switch boundary

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

735 case {'w', 'e'}

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

736 switch comp_str

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

737 case 'normal'

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

738 comp = 1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

739 case 'tangential'

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

740 comp = 2;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

741 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

742 case {'s', 'n'}

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

743 switch comp_str

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

744 case 'normal'

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

745 comp = 2;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

746 case 'tangential'

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

747 comp = 1;

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

748 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

749 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

750 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

751

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

752 % Returns h11 for the boundary specified by the string boundary.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

753 % op -- string

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

754 function [h11, theta_R] = getBorrowing(obj, boundary)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

755 assertIsMember(boundary, {'w', 'e', 's', 'n'})

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

756

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

757 switch boundary

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

758 case {'w','e'}

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

759 h11 = obj.h11{1};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

760 theta_R = obj.theta_R{1};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

761 case {'s', 'n'}

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

762 h11 = obj.h11{2};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

763 theta_R = obj.theta_R{2};

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

764 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

765 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

766

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

767 % Returns the outward unit normal vector for the boundary specified by the string boundary.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

768 function nu = getNormal(obj, boundary)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

769 assertIsMember(boundary, {'w', 'e', 's', 'n'})

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

770

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

771 switch boundary

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

772 case 'w'

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

773 nu = [-1,0];

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

774 case 'e'

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

775 nu = [1,0];

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

776 case 's'

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

777 nu = [0,-1];

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

778 case 'n'

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

779 nu = [0,1];

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

780 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

781 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

782

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

783 % Returns the boundary operator op for the boundary specified by the string boundary.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

784 % op -- string

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

785 function o = getBoundaryOperator(obj, op, boundary)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

786 assertIsMember(boundary, {'w', 'e', 's', 'n'})

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

787 assertIsMember(op, {'e', 'e1', 'e2', 'tau', 'tau1', 'tau2'})

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

788

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

789 switch op

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

790 case {'e', 'e1', 'e2', 'tau', 'tau1', 'tau2'}

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

791 o = obj.([op, '_', boundary]);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

792 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

793

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

794 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

795

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

796 % Returns the boundary operator op for the boundary specified by the string boundary.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

797 % op -- string

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

798 function o = getBoundaryOperatorForScalarField(obj, op, boundary)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

799 assertIsMember(boundary, {'w', 'e', 's', 'n'})

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

800 assertIsMember(op, {'e', 'e_shifted'})

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

801

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

802 switch op

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

803

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

804 case 'e'

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

805 o = obj.(['e_scalar', '_', boundary]);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

806 case 'e_shifted'

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

807 o = obj.(['e_shifted_scalar', '_', boundary]);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

808 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

809

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

810 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

811

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

812 % Returns the boundary operator T_ij (cell format) for the boundary specified by the string boundary.

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

813 % Formula: tau_i = T_ij u_j

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

814 % op -- string

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

815 function T = getBoundaryTractionOperator(obj, boundary)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

816 assertIsMember(boundary, {'w', 'e', 's', 'n'})

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

817

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

818 T = obj.(['T', '_', boundary]);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

819 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

820

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

821 % Returns square boundary quadrature matrix, of dimension

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

822 % corresponding to the number of boundary unknowns

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

823 %

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

824 % boundary -- string

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

825 function H = getBoundaryQuadrature(obj, boundary)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

826 assertIsMember(boundary, {'w', 'e', 's', 'n'})

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

827

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

828 H = obj.getBoundaryQuadratureForScalarField(boundary);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

829 I_dim = speye(obj.dim, obj.dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

830 H = kron(H, I_dim);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

831 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

832

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

833 % Returns square boundary quadrature matrix, of dimension

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

834 % corresponding to the number of boundary grid points

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

835 %

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

836 % boundary -- string

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

837 function H_b = getBoundaryQuadratureForScalarField(obj, boundary)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

838 assertIsMember(boundary, {'w', 'e', 's', 'n'})

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

839

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

840 H_b = obj.(['H_', boundary]);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

841 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

842

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

843 function N = size(obj)

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

844 N = obj.dim*prod(obj.m);

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

845 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

846 end

14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible.

Martin Almquist <martin.almquist@it.uu.se>

parents:

diff changeset

847 end

Mercurial > repos > public > sbplib

annotate +scheme/Elastic2dVariableAnisotropicIncompatible.m @ 1345:14f44e81e1e3 feature/poroelastic