sbplib: +scheme/elasticVariable.m annotate

annotate +scheme/elasticVariable.m @ 679:247b58a4dbe8 feature/poroelastic

Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments.

author	Martin Almquist <malmquist@stanford.edu>
date	Mon, 05 Feb 2018 14:45:26 -0800
parents	06676c40e77f
children	b035902869a8

rev	line source
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	1 classdef elasticVariable < scheme.Scheme
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	2
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	3 % Discretizes the elastic wave equation:
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	4 % rho u_{i,tt} = di lambda dj u_j + dj mu di u_j + dj mu dj u_i
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	5
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	6 properties
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7 m % Number of points in each direction, possibly a vector
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8 h % Grid spacing
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	10 grid
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11 dim
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13 order % Order of accuracy for the approximation
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	15 % Diagonal matrices for varible coefficients
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16 LAMBDA % Variable coefficient, related to dilation
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17 MU % Shear modulus, variable coefficient
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	18 RHO, RHOi % Density, variable
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20 D % Total operator
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21 D1 % First derivatives
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	23 % Second derivatives
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	24 D2_lambda
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25 D2_mu
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27 % Traction operators used for BC
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28 T_l, T_r
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29 tau_l, tau_r
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	30
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	31 H, Hi % Inner products
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32 phi % Borrowing constant for (d1 - e^T*D1) from R
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	33 gamma % Borrowing constant for d1 from M
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	34 H11 % First element of H
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	35 e_l, e_r
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	36 d1_l, d1_r % Normal derivatives at the boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	37 E % E{i}^T picks out component i
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	38
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	39 H_boundary % Boundary inner products
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	40
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 % Kroneckered norms and coefficients
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42 RHOi_kron
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 Hi_kron
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	45
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46 methods
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	47
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	48 function obj = elasticVariable(g ,order, lambda_fun, mu_fun, rho_fun, opSet)
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	49 default_arg('opSet',@sbp.D2Variable);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	50 default_arg('lambda_fun', @(x,y) 0*x+1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	51 default_arg('mu_fun', @(x,y) 0*x+1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	52 default_arg('rho_fun', @(x,y) 0*x+1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53 dim = 2;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55 assert(isa(g, 'grid.Cartesian'))
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	57 lambda = grid.evalOn(g, lambda_fun);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	58 mu = grid.evalOn(g, mu_fun);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	59 rho = grid.evalOn(g, rho_fun);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	60 m = g.size();
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	61 m_tot = g.N();
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	62
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	63 h = g.scaling();
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	64 L = (m-1).*h;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	65
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	66 % 1D operators
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	67 ops = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	68 for i = 1:dim
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	69 ops{i} = opSet(m(i), {0, L(i)}, order);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	70 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	71
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	72 % Borrowing constants
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	73 beta = ops{1}.borrowing.R.delta_D;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	74 obj.H11 = ops{1}.borrowing.H11;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	75 obj.phi = beta/obj.H11;
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	76 obj.gamma = ops{1}.borrowing.M.d1;
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	77
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	78 I = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	79 D1 = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	80 D2 = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81 H = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	82 Hi = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	83 e_l = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	84 e_r = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	85 d1_l = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	86 d1_r = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	87
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	88 for i = 1:dim
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	89 I{i} = speye(m(i));
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	90 D1{i} = ops{i}.D1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	91 D2{i} = ops{i}.D2;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	92 H{i} = ops{i}.H;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	93 Hi{i} = ops{i}.HI;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	94 e_l{i} = ops{i}.e_l;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	95 e_r{i} = ops{i}.e_r;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	96 d1_l{i} = ops{i}.d1_l;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	97 d1_r{i} = ops{i}.d1_r;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	98 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	99
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	100 %====== Assemble full operators ========
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	101 LAMBDA = spdiag(lambda);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	102 obj.LAMBDA = LAMBDA;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	103 MU = spdiag(mu);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	104 obj.MU = MU;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	105 RHO = spdiag(rho);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	106 obj.RHO = RHO;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	107 obj.RHOi = inv(RHO);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	108
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	109 obj.D1 = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	110 obj.D2_lambda = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	111 obj.D2_mu = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	112 obj.e_l = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	113 obj.e_r = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	114 obj.d1_l = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	115 obj.d1_r = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	116
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	117 % D1
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	118 obj.D1{1} = kron(D1{1},I{2});
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	119 obj.D1{2} = kron(I{1},D1{2});
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	120
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	121 % Boundary operators
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	122 obj.e_l{1} = kron(e_l{1},I{2});
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	123 obj.e_l{2} = kron(I{1},e_l{2});
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	124 obj.e_r{1} = kron(e_r{1},I{2});
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	125 obj.e_r{2} = kron(I{1},e_r{2});
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	126
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	127 obj.d1_l{1} = kron(d1_l{1},I{2});
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	128 obj.d1_l{2} = kron(I{1},d1_l{2});
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	129 obj.d1_r{1} = kron(d1_r{1},I{2});
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	130 obj.d1_r{2} = kron(I{1},d1_r{2});
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	131
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	132 % D2
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	133 for i = 1:dim
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	134 obj.D2_lambda{i} = sparse(m_tot);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	135 obj.D2_mu{i} = sparse(m_tot);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	136 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137 ind = grid.funcToMatrix(g, 1:m_tot);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	138
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	139 for i = 1:m(2)
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	140 D_lambda = D2{1}(lambda(ind(:,i)));
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	141 D_mu = D2{1}(mu(ind(:,i)));
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	142
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	143 p = ind(:,i);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	144 obj.D2_lambda{1}(p,p) = D_lambda;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	145 obj.D2_mu{1}(p,p) = D_mu;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	146 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	147
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	148 for i = 1:m(1)
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	149 D_lambda = D2{2}(lambda(ind(i,:)));
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	150 D_mu = D2{2}(mu(ind(i,:)));
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	151
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	152 p = ind(i,:);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	153 obj.D2_lambda{2}(p,p) = D_lambda;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	154 obj.D2_mu{2}(p,p) = D_mu;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	155 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	156
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	157 % Quadratures
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	158 obj.H = kron(H{1},H{2});
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	159 obj.Hi = inv(obj.H);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	160 obj.H_boundary = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	161 obj.H_boundary{1} = H{2};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	162 obj.H_boundary{2} = H{1};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	163
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	164 % E{i}^T picks out component i.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	165 E = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	166 I = speye(m_tot,m_tot);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	167 for i = 1:dim
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	168 e = sparse(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	169 e(i) = 1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	170 E{i} = kron(I,e);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	171 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	172 obj.E = E;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	173
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	174 % Differentiation matrix D (without SAT)
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	175 D2_lambda = obj.D2_lambda;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	176 D2_mu = obj.D2_mu;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	177 D1 = obj.D1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178 D = sparse(dimm_tot,dimm_tot);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	179 d = @kroneckerDelta; % Kronecker delta
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	180 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	181 for i = 1:dim
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	182 for j = 1:dim
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	183 D = D + E{i}inv(RHO)( d(i,j)D2_lambda{i}E{j}' +...
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	184 db(i,j)D1{i}LAMBDAD1{j}E{j}' ...
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	185 );
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	186 D = D + E{i}inv(RHO)( d(i,j)D2_mu{i}E{j}' +...
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	187 db(i,j)D1{j}MUD1{i}E{j}' + ...
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	188 D2_mu{j}*E{i}' ...
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	189 );
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	191 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	192 obj.D = D;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	193 %=========================================%
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	194
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	195 % Numerical traction operators for BC.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	196 % Because d1 =/= e0^T*D1, the numerical tractions are different
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	197 % at every boundary.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	198 T_l = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	199 T_r = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	200 tau_l = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	201 tau_r = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	202 % tau^{j}_i = sum_k T^{j}_{ik} u_k
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	203
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	204 d1_l = obj.d1_l;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	205 d1_r = obj.d1_r;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	206 e_l = obj.e_l;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	207 e_r = obj.e_r;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	208 D1 = obj.D1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	209
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	210 % Loop over boundaries
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	211 for j = 1:dim
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	212 T_l{j} = cell(dim,dim);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	213 T_r{j} = cell(dim,dim);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	214 tau_l{j} = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	215 tau_r{j} = cell(dim,1);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	216
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	217 % Loop over components
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	218 for i = 1:dim
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	219 tau_l{j}{i} = sparse(m_tot,dim*m_tot);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	220 tau_r{j}{i} = sparse(m_tot,dim*m_tot);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	221 for k = 1:dim
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	222 T_l{j}{i,k} = ...
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 -d(i,j)LAMBDA(d(i,k)e_l{k}d1_l{k}' + db(i,k)*D1{k})...
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	224 -d(j,k)MU(d(i,j)e_l{i}d1_l{i}' + db(i,j)*D1{i})...
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	225 -d(i,k)MUe_l{j}*d1_l{j}';
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	226
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	227 T_r{j}{i,k} = ...
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	228 d(i,j)LAMBDA(d(i,k)e_r{k}d1_r{k}' + db(i,k)*D1{k})...
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	229 +d(j,k)MU(d(i,j)e_r{i}d1_r{i}' + db(i,j)*D1{i})...
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	230 +d(i,k)MUe_r{j}*d1_r{j}';
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	231
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	232 tau_l{j}{i} = tau_l{j}{i} + T_l{j}{i,k}*E{k}';
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	233 tau_r{j}{i} = tau_r{j}{i} + T_r{j}{i,k}*E{k}';
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	234 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	235
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	237 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	238 obj.T_l = T_l;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	239 obj.T_r = T_r;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	240 obj.tau_l = tau_l;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	241 obj.tau_r = tau_r;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	242
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	243 % Kroneckered norms and coefficients
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	244 I_dim = speye(dim);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	245 obj.RHOi_kron = kron(obj.RHOi, I_dim);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	246 obj.Hi_kron = kron(obj.Hi, I_dim);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	247
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	248 % Misc.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	249 obj.m = m;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	250 obj.h = h;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	251 obj.order = order;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	252 obj.grid = g;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	253 obj.dim = dim;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	254
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	255 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	256
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	257
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	258 % Closure functions return the operators applied to the own domain to close the boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	259 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	260 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	261 % type is a cell array of strings specifying the type of boundary condition for each component.
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	262 % data is a function returning the data that should be applied at the boundary.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	263 % neighbour_scheme is an instance of Scheme that should be interfaced to.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	264 % neighbour_boundary is a string specifying which boundary to interface to.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	265 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	266 default_arg('type',{'free','free'});
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	267 default_arg('parameter', []);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	268
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	269 % j is the coordinate direction of the boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	270 % nj: outward unit normal component.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	271 % nj = -1 for west, south, bottom boundaries
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	272 % nj = 1 for east, north, top boundaries
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	273 [j, nj] = obj.get_boundary_number(boundary);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	274 switch nj
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	275 case 1
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	276 e = obj.e_r;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	277 d = obj.d1_r;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	278 tau = obj.tau_r{j};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	279 T = obj.T_r{j};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	280 case -1
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	281 e = obj.e_l;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	282 d = obj.d1_l;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	283 tau = obj.tau_l{j};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	284 T = obj.T_l{j};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	287 E = obj.E;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	288 Hi = obj.Hi;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	289 H_gamma = obj.H_boundary{j};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	290 LAMBDA = obj.LAMBDA;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	291 MU = obj.MU;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	292 RHOi = obj.RHOi;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	293
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	294 dim = obj.dim;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	295 m_tot = obj.grid.N();
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	296
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	297 RHOi_kron = obj.RHOi_kron;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	298 Hi_kron = obj.Hi_kron;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	299
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	300 % Preallocate
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	301 closure = sparse(dimm_tot, dimm_tot);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	302 penalty = cell(dim,1);
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	303 for k = 1:dim
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	304 penalty{k} = sparse(dim*m_tot, m_tot/obj.m(j));
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	305 end
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	306
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	307 % Loop over components that we (potentially) have different BC on
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	308 for k = 1:dim
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	309 switch type{k}
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	310
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	311 % Dirichlet boundary condition
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	312 case {'D','d','dirichlet','Dirichlet'}
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	313
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	314 tuning = 1.2;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	315 phi = obj.phi;
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	316 h = obj.h(j);
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	317 h11 = obj.H11*h;
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	318 gamma = obj.gamma;
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	319
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	320 a_lambda = dim/h11 + 1/(h11*phi);
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	321 a_mu_i = 2/(gamma*h);
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	322 a_mu_ij = 2/h11 + 1/(h11*phi);
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	323
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	324 d = @kroneckerDelta; % Kronecker delta
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	325 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	326 alpha = @(i,j) tuning( d(i,j) a_lambda*LAMBDA ...
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	327 + d(i,j)* a_mu_i*MU ...
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	328 + db(i,j)a_mu_ijMU );
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	329
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	330 % Loop over components that Dirichlet penalties end up on
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	331 for i = 1:dim
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	332 C = T{k,i};
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	333 A = -d(i,k)*alpha(i,j);
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	334 B = A + C;
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	335 closure = closure + E{i}RHOiHiB'e{j}H_gamma(e{j}'*E{k}' );
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	336 penalty{k} = penalty{k} - E{i}RHOiHiB'e{j}*H_gamma;
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	337 end
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	338
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	339 % Free boundary condition
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	340 case {'F','f','Free','free','traction','Traction','t','T'}
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	341 closure = closure - E{k}RHOiHie{j}H_gamma* (e{j}'*tau{k} );
247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	342 penalty{k} = penalty{k} + E{k}RHOiHie{j}H_gamma;
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	343
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344 % Unknown boundary condition
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	345 otherwise
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346 error('No such boundary condition: type = %s',type);
679 247b58a4dbe8 Add support for Dirichlet and Traction BC on different components at the same boundary. Remove some unused variables and improve comments. Martin Almquist <malmquist@stanford.edu> parents: 678 diff changeset	347 end
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	348 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	349 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	351 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352 % u denotes the solution in the own domain
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	353 % v denotes the solution in the neighbour domain
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	354 tuning = 1.2;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	355 % tuning = 20.2;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	356 error('Interface not implemented');
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	357 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	358
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	359 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	360 function [j, nj] = get_boundary_number(obj, boundary)
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	361
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	362 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	363 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	364 j = 1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	365 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	366 j = 2;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	367 otherwise
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	368 error('No such boundary: boundary = %s',boundary);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	369 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	370
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	371 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	372 case {'w','W','west','West','s','S','south','South'}
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	373 nj = -1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	374 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	375 nj = 1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	376 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	377 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	378
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	379 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	380 function [return_op] = get_boundary_operator(obj, op, boundary)
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	381
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	382 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	384 j = 1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	385 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	386 j = 2;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	387 otherwise
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	388 error('No such boundary: boundary = %s',boundary);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	389 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	390
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	391 switch op
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	392 case 'e'
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	393 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	394 case {'w','W','west','West','s','S','south','South'}
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	395 return_op = obj.e_l{j};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	396 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	397 return_op = obj.e_r{j};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	398 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	399 case 'd'
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	400 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	401 case {'w','W','west','West','s','S','south','South'}
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	402 return_op = obj.d_l{j};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	403 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	404 return_op = obj.d_r{j};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	405 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	406 otherwise
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	407 error(['No such operator: operatr = ' op]);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	408 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	409
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	410 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	411
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	412 function N = size(obj)
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	413 N = prod(obj.m);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	414 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	415 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	416 end

Mercurial > repos > public > sbplib

annotate +scheme/elasticVariable.m @ 679:247b58a4dbe8 feature/poroelastic