sbplib: +scheme/Elastic2dVariableAnisotropic.m annotate

author	Martin Almquist <malmquist@stanford.edu>
date	Thu, 05 Sep 2019 14:13:00 -0700
parents
children	31d7288d0653

rev	line source
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	1 classdef Elastic2dVariableAnisotropic < scheme.Scheme
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	2
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	3 % Discretizes the elastic wave equation:
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	4 % rho u_{i,tt} = dj C_{ijkl} dk u_j
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	5 % opSet should be cell array of opSets, one per dimension. This
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	6 % is useful if we have periodic BC in one direction.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7 % Assumes fully compatible operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9 properties
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	10 m % Number of points in each direction, possibly a vector
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11 h % Grid spacing
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13 grid
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14 dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	15
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16 order % Order of accuracy for the approximation
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	18 % Diagonal matrices for variable coefficients
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19 RHO, RHOi, RHOi_kron % Density
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20 C % Elastic stiffness tensor
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22 D % Total operator
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	23 D1 % First derivatives
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	24 D2 % Second derivatives
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 % Boundary operators in cell format, used for BC
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27 T_w, T_e, T_s, T_n
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29 % Traction operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	30 tau_w, tau_e, tau_s, tau_n % Return vector field
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	31 tau1_w, tau1_e, tau1_s, tau1_n % Return scalar field
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32 tau2_w, tau2_e, tau2_s, tau2_n % Return scalar field
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	33
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	34 % Inner products
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	35 H, Hi, Hi_kron, H_1D
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	36
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	37 % Boundary inner products (for scalar field)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	38 H_w, H_e, H_s, H_n
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	39
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	40 % Boundary restriction operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 e_w, e_e, e_s, e_n % Act on vector field, return vector field at boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42 e1_w, e1_e, e1_s, e1_n % Act on vector field, return scalar field at boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 e2_w, e2_e, e2_s, e2_n % Act on vector field, return scalar field at boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44 e_scalar_w, e_scalar_e, e_scalar_s, e_scalar_n; % Act on scalar field, return scalar field
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	45
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46 % E{i}^T picks out component i
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	47 E
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	48
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	49 % Borrowing constants of the form gamma*h, where gamma is a dimensionless constant.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	50 h11 % First entry in norm matrix
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	51
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	52 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54 methods
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56 % The coefficients can either be function handles or grid functions
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	57 % optFlag -- if true, extra computations are performed, which may be helpful for optimization.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	58 function obj = Elastic2dVariableAnisotropic(g, order, rho, C, opSet, optFlag)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	59 default_arg('rho', @(x,y) 0*x+1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	60 default_arg('opSet',{@sbp.D2VariableCompatible, @sbp.D2VariableCompatible});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	61 default_arg('optFlag', false);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	62 dim = 2;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	63
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	64 C_default = cell(dim,dim,dim,dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	65 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	66 for j = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	67 for k = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	68 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	69 C_default{i,j,k,l} = @(x,y) 0*x + 1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	70 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	71 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	72 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	73 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	74 default_arg('C', C_default);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	75 assert(isa(g, 'grid.Cartesian'))
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	76
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	77 if isa(rho, 'function_handle')
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	78 rho = grid.evalOn(g, rho);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	79 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	80
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81 C_mat = cell(dim,dim,dim,dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	82 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	83 for j = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	84 for k = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	85 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	86 if isa(C{i,j,k,l}, 'function_handle')
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	87 C{i,j,k,l} = grid.evalOn(g, C{i,j,k,l});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	88 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	89 C_mat{i,j,k,l} = spdiag(C{i,j,k,l});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	90 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	91 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	92 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	93 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	94 obj.C = C_mat;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	95
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	96 m = g.size();
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	97 m_tot = g.N();
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	98 lim = g.lim;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	99 if isempty(lim)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	100 x = g.x;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	101 lim = cell(length(x),1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	102 for i = 1:length(x)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	103 lim{i} = {min(x{i}), max(x{i})};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	104 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	105 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	106
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	107 % 1D operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	108 ops = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	109 h = zeros(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	110 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	111 ops{i} = opSet{i}(m(i), lim{i}, order);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	112 h(i) = ops{i}.h;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	113 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	114
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	115 % Borrowing constants
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	116 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	117 obj.h11{i} = h(i)*ops{i}.borrowing.H11;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	118 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	119
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	120 I = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	121 D1 = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	122 D2 = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	123 H = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	124 Hi = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	125 e_0 = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	126 e_m = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	127 d1_0 = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	128 d1_m = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	129
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	130 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	131 I{i} = speye(m(i));
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	132 D1{i} = ops{i}.D1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	133 D2{i} = ops{i}.D2;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	134 H{i} = ops{i}.H;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	135 Hi{i} = ops{i}.HI;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	136 e_0{i} = ops{i}.e_l;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137 e_m{i} = ops{i}.e_r;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	138 d1_0{i} = ops{i}.d1_l;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	139 d1_m{i} = ops{i}.d1_r;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	140 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	141
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	142 %====== Assemble full operators ========
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	143 RHO = spdiag(rho);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	144 obj.RHO = RHO;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	145 obj.RHOi = inv(RHO);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	146
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	147 obj.D1 = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	148 obj.D2 = cell(dim,dim,dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	149
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	150 % D1
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	151 obj.D1{1} = kron(D1{1},I{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	152 obj.D1{2} = kron(I{1},D1{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	153
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	154 % Boundary restriction operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	155 e_l = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	156 e_r = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	157 e_l{1} = kron(e_0{1}, I{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	158 e_l{2} = kron(I{1}, e_0{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	159 e_r{1} = kron(e_m{1}, I{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	160 e_r{2} = kron(I{1}, e_m{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	161
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	162 e_scalar_w = e_l{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	163 e_scalar_e = e_r{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	164 e_scalar_s = e_l{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	165 e_scalar_n = e_r{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	166
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	167 I_dim = speye(dim, dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	168 e_w = kron(e_scalar_w, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	169 e_e = kron(e_scalar_e, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	170 e_s = kron(e_scalar_s, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	171 e_n = kron(e_scalar_n, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	172
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	173 % E{i}^T picks out component i.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	174 E = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	175 I = speye(m_tot,m_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	176 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	177 e = sparse(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178 e(i) = 1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	179 E{i} = kron(I,e);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	180 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	181 obj.E = E;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	182
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	183 e1_w = (e_scalar_w'*E{1}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	184 e1_e = (e_scalar_e'*E{1}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	185 e1_s = (e_scalar_s'*E{1}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	186 e1_n = (e_scalar_n'*E{1}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	187
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	188 e2_w = (e_scalar_w'*E{2}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	189 e2_e = (e_scalar_e'*E{2}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190 e2_s = (e_scalar_s'*E{2}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	191 e2_n = (e_scalar_n'*E{2}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	192
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	193
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	194 % D2
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	195 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	196 for k = 2:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	197 for l = 2:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	198 obj.D2{i,k,l} = sparse(m_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	199 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	200 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	201 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	202 ind = grid.funcToMatrix(g, 1:m_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	203
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	204 k = 1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	205 for r = 1:m(2)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	206 p = ind(:,r);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	207 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	208 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	209 coeff = C{i,k,k,l};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	210 D_kk = D2{1}(coeff(p));
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	211 obj.D2{i,k,l}(p,p) = D_kk;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	212 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	213 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	214 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	215
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	216 k = 2;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	217 for r = 1:m(1)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	218 p = ind(r,:);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	219 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	220 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	221 coeff = C{i,k,k,l};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	222 D_kk = D2{2}(coeff(p));
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 obj.D2{i,k,l}(p,p) = D_kk;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	224 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	225 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	226 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	227
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	228 % Quadratures
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	229 obj.H = kron(H{1},H{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	230 obj.Hi = inv(obj.H);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	231 obj.H_w = H{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	232 obj.H_e = H{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	233 obj.H_s = H{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	234 obj.H_n = H{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	235 obj.H_1D = {H{1}, H{2}};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	237 % Differentiation matrix D (without SAT)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	238 D2 = obj.D2;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	239 D1 = obj.D1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	240 D = sparse(dimm_tot,dimm_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	241 d = @kroneckerDelta; % Kronecker delta
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	242 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	243 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	244 for j = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	245 for k = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	246 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	247 D = D + E{i}inv(RHO)( d(j,k)D2{i,k,l}E{l}' +...
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	248 db(j,k)D1{j}C_mat{i,j,k,l}D1{k}E{l}' ...
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	249 );
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	250 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	251 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	252 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	253 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	254 obj.D = D;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	255 %=========================================%'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	256
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	257 % Numerical traction operators for BC.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	258 %
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	259 % Formula at boundary j: % tau^{j}_i = sum_l T^{j}_{il} u_l
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	260 %
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	261 T_l = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	262 T_r = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	263 tau_l = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	264 tau_r = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	265
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	266 D1 = obj.D1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	267
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	268 % Boundary j
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	269 for j = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	270 T_l{j} = cell(dim,dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	271 T_r{j} = cell(dim,dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	272 tau_l{j} = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	273 tau_r{j} = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	274
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	275 [~, n_l] = size(e_l{j});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	276 [~, n_r] = size(e_r{j});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	277
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	278 % Traction component i
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	279 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	280 tau_l{j}{i} = sparse(dim*m_tot, n_l);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	281 tau_r{j}{i} = sparse(dim*m_tot, n_r);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	282
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	283 % Displacement component l
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	284 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 T_l{j}{i,l} = sparse(m_tot, n_l);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286 T_r{j}{i,l} = sparse(m_tot, n_r);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	287
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	288 % Derivative direction k
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	289 for k = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	290 T_l{j}{i,l} = T_l{j}{i,l} ...
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	291 - (e_l{j}'C_mat{i,j,k,l}D1{k})';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	292 T_r{j}{i,l} = T_r{j}{i,l} ...
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	293 + (e_r{j}'C_mat{i,j,k,l}D1{k})';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	294 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	295 tau_l{j}{i} = tau_l{j}{i} + (T_l{j}{i,l}'*E{l}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	296 tau_r{j}{i} = tau_r{j}{i} + (T_r{j}{i,l}'*E{l}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	297 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	298 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	299 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	300
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	301 % Traction tensors, T_ij
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	302 obj.T_w = T_l{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	303 obj.T_e = T_r{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	304 obj.T_s = T_l{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	305 obj.T_n = T_r{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	306
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	307 % Restriction operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	308 obj.e_w = e_w;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	309 obj.e_e = e_e;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	310 obj.e_s = e_s;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	311 obj.e_n = e_n;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	312
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	313 obj.e1_w = e1_w;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	314 obj.e1_e = e1_e;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	315 obj.e1_s = e1_s;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	316 obj.e1_n = e1_n;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	317
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	318 obj.e2_w = e2_w;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	319 obj.e2_e = e2_e;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	320 obj.e2_s = e2_s;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	321 obj.e2_n = e2_n;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	322
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	323 obj.e_scalar_w = e_scalar_w;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	324 obj.e_scalar_e = e_scalar_e;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	325 obj.e_scalar_s = e_scalar_s;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	326 obj.e_scalar_n = e_scalar_n;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	327
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	328 % First component of traction
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	329 obj.tau1_w = tau_l{1}{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	330 obj.tau1_e = tau_r{1}{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	331 obj.tau1_s = tau_l{2}{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	332 obj.tau1_n = tau_r{2}{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	333
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	334 % Second component of traction
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	335 obj.tau2_w = tau_l{1}{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	336 obj.tau2_e = tau_r{1}{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	337 obj.tau2_s = tau_l{2}{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	338 obj.tau2_n = tau_r{2}{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	339
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	340 % Traction vectors
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	341 obj.tau_w = (e_w'e1_wobj.tau1_w')' + (e_w'e2_wobj.tau2_w')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	342 obj.tau_e = (e_e'e1_eobj.tau1_e')' + (e_e'e2_eobj.tau2_e')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	343 obj.tau_s = (e_s'e1_sobj.tau1_s')' + (e_s'e2_sobj.tau2_s')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344 obj.tau_n = (e_n'e1_nobj.tau1_n')' + (e_n'e2_nobj.tau2_n')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	345
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346 % Kroneckered norms and coefficients
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	347 obj.RHOi_kron = kron(obj.RHOi, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	348 obj.Hi_kron = kron(obj.Hi, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	349
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350 % Misc.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	351 obj.m = m;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352 obj.h = h;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	353 obj.order = order;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	354 obj.grid = g;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	355 obj.dim = dim;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	356
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	357 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	358
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	359
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	360 % Closure functions return the operators applied to the own domain to close the boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	361 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	362 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	363 % bc is a cell array of component and bc type, e.g. {1, 'd'} for Dirichlet condition
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	364 % on the first component. Can also be e.g.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	365 % {'normal', 'd'} or {'tangential', 't'} for conditions on
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	366 % tangential/normal component.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	367 % data is a function returning the data that should be applied at the boundary.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	368 % neighbour_scheme is an instance of Scheme that should be interfaced to.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	369 % neighbour_boundary is a string specifying which boundary to interface to.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	370 function [closure, penalty] = boundary_condition(obj, boundary, bc, tuning)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	371 default_arg('tuning', 1.0);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	372
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	373 assert( iscell(bc), 'The BC type must be a 2x1 cell array' );
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	374 comp = bc{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	375 type = bc{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	376 if ischar(comp)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	377 comp = obj.getComponent(comp, boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	378 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	379
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	380 e = obj.getBoundaryOperatorForScalarField('e', boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	381 tau = obj.getBoundaryOperator(['tau' num2str(comp)], boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	382 T = obj.getBoundaryTractionOperator(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383 h11 = obj.getBorrowing(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	384 H_gamma = obj.getBoundaryQuadratureForScalarField(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	385 nu = obj.getNormal(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	386
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	387 E = obj.E;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	388 Hi = obj.Hi;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	389 RHOi = obj.RHOi;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	390 C = obj.C;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	391
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	392 dim = obj.dim;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	393 m_tot = obj.grid.N();
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	394
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	395 % Preallocate
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	396 [~, col] = size(tau);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	397 closure = sparse(dimm_tot, dimm_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	398 penalty = sparse(dim*m_tot, col);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	399
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	400 j = comp;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	401 switch type
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	402
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	403 % Dirichlet boundary condition
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	404 % OBS! Cannot yet set one component at a time unless one assumes Displacement for all components
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	405 case {'D','d','dirichlet','Dirichlet','displacement','Displacement'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	406
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	407 % Loop over components that Dirichlet penalties end up on
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	408 % Y: symmetrizing part of penalty
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	409 % Z: symmetric part of penalty
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	410 % X = Y + Z.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	411 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	412 Y = T{j,i}';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	413
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	414 Z = sparse(m_tot, m_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	415 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	416 for k = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	417 Z = Z + nu(l)C{i,l,k,j}nu(k);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	418 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	419 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	420 Z = -tuningdim/h11Z;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	421 X = Z + e*Y;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	422 closure = closure + E{i}RHOiHiX'eH_gamma(e'*E{j}' );
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	423 penalty = penalty - E{i}RHOiHiX'e*H_gamma;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	424 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	425
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	426 % Free boundary condition
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	427 case {'F','f','Free','free','traction','Traction','t','T'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	428 closure = closure - E{j}RHOiHieH_gamma*tau';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	429 penalty = penalty + E{j}RHOiHieH_gamma;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	430
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	431 % Unknown boundary condition
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	432 otherwise
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	433 error('No such boundary condition: type = %s',type);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	434 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	435 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	436
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	437 % type Struct that specifies the interface coupling.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	438 % Fields:
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	439 % -- tuning: penalty strength, defaults to 1.2
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	440 % -- interpolation: type of interpolation, default 'none'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	441 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	442
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	443 defaultType.tuning = 1.2;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	444 defaultType.interpolation = 'none';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	445 default_struct('type', defaultType);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	446
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	447 switch type.interpolation
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	448 case {'none', ''}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	449 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	450 case {'op','OP'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	451 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	452 otherwise
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	453 error('Unknown type of interpolation: %s ', type.interpolation);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	454 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	455 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	456
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	457 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	458 tuning = type.tuning;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	459
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	460 % u denotes the solution in the own domain
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	461 % v denotes the solution in the neighbour domain
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	462 % Operators without subscripts are from the own domain.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	463
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	464 % Get boundary operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	465 e = obj.getBoundaryOperator('e', boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	466 tau = obj.getBoundaryOperator('tau', boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	467
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	468 e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	469 tau_v = neighbour_scheme.getBoundaryOperator('tau', neighbour_boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	470
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	471 H_gamma = obj.getBoundaryQuadrature(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	472
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	473 % Operators and quantities that correspond to the own domain only
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	474 Hi = obj.Hi_kron;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	475 RHOi = obj.RHOi_kron;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	476
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	477 % Penalty strength operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	478 alpha_u = 1/4tuningobj.getBoundaryOperator('alpha', boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	479 alpha_v = 1/4tuningneighbour_scheme.getBoundaryOperator('alpha', neighbour_boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	480
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	481 closure = -RHOiHieH_gamma(alpha_u' + alpha_v'e_ve');
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	482 penalty = RHOiHieH_gamma(alpha_u'ee_v' + alpha_v');
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	483
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	484 closure = closure - 1/2RHOiHieH_gamma*tau';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	485 penalty = penalty - 1/2RHOiHieH_gamma*tau_v';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	486
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	487 closure = closure + 1/2RHOiHitauH_gamma*e';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	488 penalty = penalty - 1/2RHOiHitauH_gamma*e_v';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	489
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	490 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	491
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	492 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	493 error('Non-conforming interfaces not implemented yet.');
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	494 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	495
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	496 % Returns the component number that is the tangential/normal component
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	497 % at the specified boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	498 function comp = getComponent(obj, comp_str, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	499 assertIsMember(comp_str, {'normal', 'tangential'});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	500 assertIsMember(boundary, {'w', 'e', 's', 'n'});

1201

8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic