sbplib: +scheme/Elastic2dVariableAnisotropicIncompatible.m annotate

annotate +scheme/Elastic2dVariableAnisotropicIncompatible.m @ 1346:464e6f65c2c6 feature/poroelastic

Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R.

author	Martin Almquist <martin.almquist@it.uu.se>
date	Tue, 30 Apr 2024 14:18:47 +0200
parents	14f44e81e1e3
children	ac54767ae1fb

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
1346 464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	53 nBP_R % Number of boundary points in R, related to borrowing from R.
1345 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;
1346 464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	127 nBP_R = 2;
1345 14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	128 case 4
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	129 width = 5;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	130 nBP = 6;
1346 464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	131 nBP_R = 4;
1345 14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	132 case 6
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	133 width = 7;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	134 nBP = 9;
1346 464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	135 nBP_R = 7;
1345 14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	136 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	137
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	138 I = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	139 D1 = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	140 D2 = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	141 H = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	142 Hi = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	143 e_0 = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	144 e_m = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	145 d1_0 = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	146 d1_m = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	147
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	148 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	149 I{i} = speye(m(i));
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	150 D1{i} = ops{i}.D1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	151 D2{i} = ops{i}.D2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	152 H{i} = ops{i}.H;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	153 Hi{i} = ops{i}.HI;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	154 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	155 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	156 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	157 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	158 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	159
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	160 %====== Assemble full operators ========
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	161 I_dim = speye(dim, dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	162 RHO = spdiag(rho);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	163 obj.RHO = RHO;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	164 obj.RHOi = inv(RHO);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	165 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	166
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	167 obj.D1 = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	168 D2_temp = cell(dim,dim,dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	169
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	170 % D1
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	171 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	172 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	173
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	174 % Boundary restriction operators
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	175 e_l = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	176 e_r = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	177 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	178 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	179 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	180 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	181
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	182 e_scalar_w = e_l{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	183 e_scalar_e = e_r{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	184 e_scalar_s = e_l{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	185 e_scalar_n = e_r{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	186
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	187 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	188 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	189 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	190 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	191
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	192 % Boundary restriction, shifted up to nBP-1 points
1346 464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	193 e_shifted_scalar_w = cell(nBP_R, 1);
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	194 e_shifted_scalar_e = cell(nBP_R, 1);
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	195 e_shifted_scalar_s = cell(nBP_R, 1);
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	196 e_shifted_scalar_n = cell(nBP_R, 1);
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	197 for i = 1:nBP_R-1
1345 14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	198 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	199 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	200 e_0_nBP{1}(i) = 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	201 e_0_nBP{2}(i) = 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	202 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	203 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	204 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	205 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	206 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	207 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	208 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	209
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	210 % Boundary derivatives
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	211 d1_l = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	212 d1_r = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	213 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	214 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	215 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	216 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	217
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	218 % 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	219 E = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	220 I = speye(m_tot,m_tot);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	221 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	222 e = sparse(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	223 e(i) = 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	224 E{i} = kron(I,e);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	225 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	226 obj.E = E;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	227
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	228 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	229 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	230 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	231 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	232
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	233 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	234 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	235 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	236 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	237
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	238 % D2
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	239 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	240 for k = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	241 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	242 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	243 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	244 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	245 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	246 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	247
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	248 k = 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	249 for r = 1:m(2)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	250 p = ind(:,r);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	251 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	252 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	253 coeff = C{k,j,k,l};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	254 D_kk = D2{1}(coeff(p));
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	255 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	256 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	257 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	258 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	259
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	260 k = 2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	261 for r = 1:m(1)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	262 p = ind(r,:);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	263 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	264 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	265 coeff = C{k,j,k,l};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	266 D_kk = D2{2}(coeff(p));
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	267 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	268 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	269 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	270 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	271
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	272 % Quadratures
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	273 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	274 obj.Hi = inv(obj.H);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	275 obj.H_w = H{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	276 obj.H_e = H{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	277 obj.H_s = H{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	278 obj.H_n = H{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	279 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	280
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	281 % Differentiation matrix D (without SAT)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	282 D1 = obj.D1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	283 D = sparse(dimm_tot,dimm_tot);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	284 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	285 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	286 for k = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	287 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	288 if i == k
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	289 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	290 D2_temp{j,k,l} = [];
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	291 else
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	292 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	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 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	296 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	297 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	298 clear D2_temp;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	299 D = obj.RHOi_kron*D;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	300 obj.D = D;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	301 clear D;
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
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	304 % Numerical traction operators for BC.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	305 %
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	306 % 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	307 %
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	308 T_l = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	309 T_r = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	310 tau_l = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	311 tau_r = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	312
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	313 D1 = obj.D1;
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 d = @kroneckerDelta; % Kronecker delta
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	316 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	317
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	318 % Boundary j
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	319 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	320 T_l{j} = cell(dim,dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	321 T_r{j} = cell(dim,dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	322 tau_l{j} = cell(dim,1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	323 tau_r{j} = cell(dim,1);
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 [~, n_l] = size(e_l{j});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	326 [~, n_r] = size(e_r{j});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	327
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	328 % Traction component i
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	329 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	330 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	331 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	332
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	333 % Displacement component l
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	334 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	335 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	336 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	337
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	338 % Derivative direction k
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	339 for k = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	340 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	341 - 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	342 - 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	343 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	344 + 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	345 + 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	346 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	347 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	348 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	349 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	350 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	351 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	352
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	353 % Traction tensors, T_ij
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	354 obj.T_w = T_l{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	355 obj.T_e = T_r{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	356 obj.T_s = T_l{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	357 obj.T_n = T_r{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	358
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	359 % Restriction operators
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	360 obj.e_w = e_w;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	361 obj.e_e = e_e;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	362 obj.e_s = e_s;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	363 obj.e_n = e_n;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	364
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	365 obj.e1_w = e1_w;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	366 obj.e1_e = e1_e;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	367 obj.e1_s = e1_s;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	368 obj.e1_n = e1_n;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	369
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	370 obj.e2_w = e2_w;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	371 obj.e2_e = e2_e;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	372 obj.e2_s = e2_s;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	373 obj.e2_n = e2_n;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	374
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	375 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	376 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	377 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	378 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	379
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	380
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	381 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	382 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	383 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	384 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	385
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	386 % First component of traction
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	387 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	388 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	389 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	390 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	391
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	392 % Second component of traction
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	393 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	394 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	395 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	396 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	397
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	398 % Traction vectors
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	399 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	400 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	401 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	402 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	403
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	404 % Kroneckered norms and coefficients
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	405 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	406
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	407 % Misc.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	408 obj.m = m;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	409 obj.h = h;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	410 obj.order = order;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	411 obj.grid = g;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	412 obj.dim = dim;
1346 464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	413 obj.nBP_R = nBP_R;
1345 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 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	416
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	417
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	418 % 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	419 % 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	420 % 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	421 % 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	422 % 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	423 % {'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	424 % tangential/normal component.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	425 % 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	426 % 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	427 % 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	428
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	429 % For displacement bc:
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	430 % bc = {comp, 'd', dComps},
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	431 % where
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	432 % 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	433 % 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	434 function [closure, penalty] = boundary_condition(obj, boundary, bc, tuning)
1346 464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	435 default_arg('tuning', 1.2);
1345 14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	436
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	437 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	438 comp = bc{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	439 type = bc{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	440 if ischar(comp)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	441 comp = obj.getComponent(comp, boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	442 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	443
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	444 e = obj.getBoundaryOperatorForScalarField('e', boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	445 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	446 T = obj.getBoundaryTractionOperator(boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	447 [h11, th_R] = obj.getBorrowing(boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	448 H_gamma = obj.getBoundaryQuadratureForScalarField(boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	449 nu = obj.getNormal(boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	450
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	451 E = obj.E;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	452 Hi = obj.Hi;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	453 RHOi = obj.RHOi;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	454 C = obj.C;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	455
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	456 dim = obj.dim;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	457 m_tot = obj.grid.N();
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	458
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	459 % Preallocate
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	460 [~, col] = size(tau);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	461 closure = sparse(dimm_tot, dimm_tot);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	462 penalty = sparse(dim*m_tot, col);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	463
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	464 j = comp;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	465 switch type
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	466
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	467 % Dirichlet boundary condition
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	468 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	469
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	470 if numel(bc) >= 3
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	471 dComps = bc{3};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	472 else
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	473 dComps = 1:dim;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	474 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	475
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	476 % 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	477 % Y: symmetrizing part of penalty
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	478 % Z: symmetric part of penalty
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	479 % X = Y + Z.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	480
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	481 % 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	482 % yield traction in discrete energy rate
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	483 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	484 Y = T{j,i}';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	485 X = e*Y;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	486 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	487 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	488 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	489
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	490 % 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	491 % (Otherwise it's not symmetric.)
1346 464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	492 beta_vec = obj.computeBorrowingFromC(boundary);
1345 14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	493 beta_inv = espdiag(1./beta_vec)e';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	494
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	495 % Compensate at corners
1346 464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	496 [~, N] = size(e);
1345 14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	497 corner_weight = ones(N, 1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	498 corner_weight(1) = 2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	499 corner_weight(end) = 2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	500 corner_weight = espdiag(corner_weight)e';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	501
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	502
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	503 % 2. Build Z.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	504 j = comp;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	505 for i = dComps
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	506 Z = sparse(m_tot, m_tot);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	507 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	508 for k = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	509 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	510 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	511 end
1346 464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	512 Z = -tuning(corner_weight/h11 + beta_inv/th_R)Z;
1345 14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	513 X = Z;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	514 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	515 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	516 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	517
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	518 % Free boundary condition
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	519 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	520 closure = closure - E{j}RHOiHieH_gamma*tau';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	521 penalty = penalty + E{j}RHOiHieH_gamma;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	522
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	523 % Unknown boundary condition
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	524 otherwise
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	525 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	526 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	527 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	528
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	529 % 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	530 % Fields:
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	531 % -- 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	532 % -- interpolation: type of interpolation, default 'none'
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	533 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	534
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	535 defaultType.tuning = 1.0;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	536 defaultType.interpolation = 'none';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	537 default_struct('type', defaultType);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	538
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	539 switch type.interpolation
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	540 case {'none', ''}
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	541 [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	542 case {'op','OP'}
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	543 [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	544 otherwise
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	545 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	546 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	547 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	548
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	549 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	550 tuning = type.tuning;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	551
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	552 % 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	553 % 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	554
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	555 u = obj;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	556 v = neighbour_scheme;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	557
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	558 % Operators, u side
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	559 e_u = u.getBoundaryOperatorForScalarField('e', boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	560 tau_u = u.getBoundaryOperator('tau', boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	561 h11_u = u.getBorrowing(boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	562 nu_u = u.getNormal(boundary);
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 E_u = u.E;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	565 C_u = u.C;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	566 m_tot_u = u.grid.N();
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	567
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	568 % Operators, v side
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	569 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	570 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	571 h11_v = v.getBorrowing(neighbour_boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	572 nu_v = v.getNormal(neighbour_boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	573
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	574 E_v = v.E;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	575 C_v = v.C;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	576 m_tot_v = v.grid.N();
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	577
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	578 % 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	579 flipFlag = false;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	580 e_v_flip = e_v;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	581 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	582 (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	583 (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	584 (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	585 (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	586 (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	587 (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	588 (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	589
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	590 flipFlag = true;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	591 e_v_flip = fliplr(e_v);
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 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	594 t2 = tau_v(:,2:2:end);
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 t1 = fliplr(t1);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	597 t2 = fliplr(t2);
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 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	600 tau_v(:,2:2:end) = t2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	601 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	602
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	603 % 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	604 Hi = u.Hi_kron;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	605 RHOi = u.RHOi_kron;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	606 e_kron = u.getBoundaryOperator('e', boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	607 T_u = u.getBoundaryTractionOperator(boundary);
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 % Shared operators
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	610 H_gamma = u.getBoundaryQuadratureForScalarField(boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	611 H_gamma_kron = u.getBoundaryQuadrature(boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	612 dim = u.dim;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	613
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	614 % Preallocate
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	615 [~, m_int] = size(H_gamma);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	616 closure = sparse(dimm_tot_u, dimm_tot_u);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	617 penalty = sparse(dimm_tot_u, dimm_tot_v);
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 % ---- Continuity of displacement ------
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	620
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	621 % Y: symmetrizing part of penalty
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	622 % Z: symmetric part of penalty
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	623 % X = Y + Z.
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	624
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	625 % 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	626 for j = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	627
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	628 % 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	629 for i = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	630 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	631 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	632 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	633 for l = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	634 for k = 1:dim
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	635 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	636 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	637 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	638 end
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 if flipFlag
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	641 Z_v = rot90(Z_v,2);
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 Z = -tuningdim( 1/(4h11_u)Z_u + 1/(4h11_v)Z_v );
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	645 X = Y + Z*e_u';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	646 closure = closure + E_u{i}X'H_gammae_u'E_u{j}';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	647 penalty = penalty - E_u{i}X'H_gammae_v_flip'E_v{j}';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	648
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	649 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	650 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	651
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	652 % ---- Continuity of traction ------
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	653 closure = closure - 1/2e_kronH_gamma_kron*tau_u';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	654 penalty = penalty - 1/2e_kronH_gamma_kron*tau_v';
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	655
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	656 % ---- 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	657 closure = RHOiHiclosure;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	658 penalty = RHOiHipenalty;
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 end
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 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	663 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	664 end
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 % Computes the largest beta such that C_b - beta*C_s >= 0, using bisection.
1346 464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	667 function beta = borrowingBisection(obj, C_b, C_s)
1345 14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	668 tol = 1e-8;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	669 beta_min = 0;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	670 beta_max = 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	671 beta = 0.5;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	672 err = (beta_max - beta_min)/2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	673 while err > tol
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	674 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	675 % 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	676 beta_max = beta;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	677 beta = (beta_min + beta)/2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	678 else
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	679 % Increase beta
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	680 beta_min = beta;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	681 beta = (beta_max + beta)/2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	682 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	683 err = err/2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	684 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	685 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	686
1346 464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	687 % Computes largest beta such that C_bJbL_boundary - \beta*C_bJbL_i >= 0, i = 0, 1, ..., nBP.
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	688 function beta = computeBorrowingFromC(obj, boundary)
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	689
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	690 e = obj.getBoundaryOperatorForScalarField('e', boundary);
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	691 e_sh = obj.getBoundaryOperatorForScalarField('e_shifted', boundary);
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	692 dim = obj.dim;
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	693
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	694 [~, N] = size(e);
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	695 beta = ones(N, 1);
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	696 b = obj.getComponent('normal', boundary);
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	697 C_boundary = cell(dim, dim, dim, dim);
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	698 for i = 1:dim
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	699 for j = 1:dim
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	700 for k = 1:dim
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	701 for l = 1:dim
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	702 C_boundary{i,j,k,l} = e'obj.C{i,j,k,l}e ;
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	703 end
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	704 end
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	705 end
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	706 end
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	707
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	708 % Loop over shift inward from boundary
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	709 for m = 1:obj.nBP_R-1
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	710 C_shifted = cell(dim, dim, dim, dim);
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	711 for i = 1:dim
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	712 for j = 1:dim
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	713 for k = 1:dim
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	714 for l = 1:dim
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	715 C_shifted{i,j,k,l} = e_sh{m}'obj.C{i,j,k,l}e_sh{m};
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	716 end
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	717 end
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	718 end
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	719 end
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	720
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	721 % Loop along boundary
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	722 for i = 1:N
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	723 C_boundary_mat = [C_boundary{b,1,b,1}(i,i), C_boundary{b,1,b,2}(i,i); ...
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	724 C_boundary{b,2,b,1}(i,i), C_boundary{b,2,b,2}(i,i)];
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	725
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	726 C_shifted_mat = [C_shifted{b,1,b,1}(i,i), C_shifted{b,1,b,2}(i,i); ...
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	727 C_shifted{b,2,b,1}(i,i), C_shifted{b,2,b,2}(i,i)];
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	728
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	729 beta_i = obj.borrowingBisection(C_boundary_mat, C_shifted_mat);
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	730 beta(i) = min(beta(i), beta_i);
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	731 end
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	732 end
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	733 if min(beta) < 1e-10
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	734 disp('WARNING! No borrowing from C seems to be possible.')
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	735 disp(['min(beta) = ' num2str(min(beta))])
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	736 end
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	737 end
464e6f65c2c6 Refactor computation of borrowing from C. Update to correct number of boundary points for borrowing from R. Martin Almquist <martin.almquist@it.uu.se> parents: 1345 diff changeset	738
1345 14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	739 % 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	740 % at the specified boundary
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	741 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	742 assertIsMember(comp_str, {'normal', 'tangential'});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	743 assertIsMember(boundary, {'w', 'e', 's', 'n'});
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	744
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	745 switch boundary
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	746 case {'w', 'e'}
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	747 switch comp_str
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	748 case 'normal'
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	749 comp = 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	750 case 'tangential'
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	751 comp = 2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	752 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	753 case {'s', 'n'}
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	754 switch comp_str
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	755 case 'normal'
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	756 comp = 2;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	757 case 'tangential'
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	758 comp = 1;
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	759 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	760 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	761 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	762
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	763 % 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	764 % op -- string
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	765 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	766 assertIsMember(boundary, {'w', 'e', 's', 'n'})
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	767
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	768 switch boundary
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	769 case {'w','e'}
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	770 h11 = obj.h11{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	771 theta_R = obj.theta_R{1};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	772 case {'s', 'n'}
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	773 h11 = obj.h11{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	774 theta_R = obj.theta_R{2};
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	775 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	776 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	777
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	778 % 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	779 function nu = getNormal(obj, boundary)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	780 assertIsMember(boundary, {'w', 'e', 's', 'n'})
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	781
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	782 switch boundary
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	783 case 'w'
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	784 nu = [-1,0];
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	785 case 'e'
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	786 nu = [1,0];
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	787 case 's'
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	788 nu = [0,-1];
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	789 case 'n'
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	790 nu = [0,1];
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	791 end
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 % 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	795 % op -- string
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	796 function o = getBoundaryOperator(obj, op, boundary)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	797 assertIsMember(boundary, {'w', 'e', 's', 'n'})
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	798 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	799
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	800 switch op
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	801 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	802 o = obj.([op, '_', boundary]);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	803 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	804
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	805 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	806
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	807 % 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	808 % op -- string
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	809 function o = getBoundaryOperatorForScalarField(obj, op, boundary)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	810 assertIsMember(boundary, {'w', 'e', 's', 'n'})
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	811 assertIsMember(op, {'e', 'e_shifted'})
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	812
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	813 switch op
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	814
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	815 case 'e'
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	816 o = obj.(['e_scalar', '_', boundary]);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	817 case 'e_shifted'
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	818 o = obj.(['e_shifted_scalar', '_', 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 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	822
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	823 % 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	824 % 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	825 % op -- string
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	826 function T = getBoundaryTractionOperator(obj, boundary)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	827 assertIsMember(boundary, {'w', 'e', 's', 'n'})
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	828
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	829 T = obj.(['T', '_', boundary]);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	830 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	831
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	832 % 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	833 % 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	834 %
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	835 % boundary -- string
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	836 function H = getBoundaryQuadrature(obj, boundary)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	837 assertIsMember(boundary, {'w', 'e', 's', 'n'})
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	838
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	839 H = obj.getBoundaryQuadratureForScalarField(boundary);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	840 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	841 H = kron(H, I_dim);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	842 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	843
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	844 % 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	845 % 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	846 %
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	847 % boundary -- string
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	848 function H_b = getBoundaryQuadratureForScalarField(obj, boundary)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	849 assertIsMember(boundary, {'w', 'e', 's', 'n'})
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	850
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	851 H_b = obj.(['H_', boundary]);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	852 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	853
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	854 function N = size(obj)
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	855 N = obj.dim*prod(obj.m);
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	856 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	857 end
14f44e81e1e3 Add scheme for Elastic2dVariable, not fully compatible. Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	858 end

Mercurial > repos > public > sbplib

annotate +scheme/Elastic2dVariableAnisotropicIncompatible.m @ 1346:464e6f65c2c6 feature/poroelastic