sbplib: +scheme/elasticVariable.m annotate

author	Martin Almquist <malmquist@stanford.edu>
date	Mon, 05 Feb 2018 11:06:15 -0800
parents
children	247b58a4dbe8

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
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7 properties
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8 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	9 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	10
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11 grid
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12 dim
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14 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	15
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16 % 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	17 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	18 MU % Shear modulus, variable coefficient
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19 RHO, RHOi % Density
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21 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	22 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	23
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	24 % Second derivatives
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25 D2_lambda
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 D2_mu
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28 % 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	29 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	30 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	31
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32 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	33 phi % Borrowing constant for (d1 - e^T*D1) from R
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 LAMBDA_boundary_l % Variable coefficients at boundaries
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42 LAMBDA_boundary_r
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 MU_boundary_l
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44 MU_boundary_r
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 % 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	47 RHOi_kron
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	48 Hi_kron
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	49 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	50
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	51 methods
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	52 % Implements the shear part of the elastic wave equation, i.e.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53 % rho u_{i,tt} = d_i a d_j u_j + d_j a d_j u_i
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54 % where a = mu.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56 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	57 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	58 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	59 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	60 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	61 dim = 2;
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 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	64
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	65 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	66 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	67 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	68 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	69 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	70
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	71 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	72 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	73
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	74 % 1D operators
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	75 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	76 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	77 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	78 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	79
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	80 % Borrowing constants
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81 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	82 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	83 obj.phi = beta/obj.H11;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	84
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	85 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	86 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	87 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	88 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	89 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	90 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	91 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	92 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	93 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	94
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	95 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	96 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	97 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	98 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	99 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	100 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	101 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	102 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	103 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	104 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	105 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	106
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	107 %====== 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	108 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	109 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	110 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	111 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	112 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	113 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	114 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	115
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	116 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	117 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	118 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	119 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	120 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	121 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	122 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	123
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	124 % D1
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	125 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	126 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	127
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	128 % Boundary operators
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	129 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	130 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	131 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	132 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	133
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	134 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	135 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	136 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	137 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	138
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	139 % D2
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	140 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	141 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	142 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	143 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	144 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	145
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	146 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	147 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	148 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	149
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	150 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	151 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	152 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	153 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	154
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	155 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	156 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	157 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	158
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	159 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	160 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	161 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	162 end
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 % Quadratures
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	165 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	166 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	167 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	168 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	169 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	170
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	171 % Boundary coefficient matrices
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	172 obj.LAMBDA_boundary_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	173 obj.LAMBDA_boundary_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	174 obj.MU_boundary_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	175 obj.MU_boundary_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	176 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	177 obj.LAMBDA_boundary_l{i} = obj.e_l{i}'LAMBDAobj.e_l{i};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178 obj.LAMBDA_boundary_r{i} = obj.e_r{i}'LAMBDAobj.e_r{i};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	179 obj.MU_boundary_l{i} = obj.e_l{i}'MUobj.e_l{i};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	180 obj.MU_boundary_r{i} = obj.e_r{i}'MUobj.e_r{i};
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	181 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	182
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	183 % 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	184 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	185 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	186 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	187 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	188 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	189 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	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 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	192
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	193 % 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	194 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	195 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	196 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	197 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	198 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	199 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	200 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	201 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	202 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	203 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	204 );
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	205 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	206 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	207 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	208 );
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	209 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	210 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	211 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	212 %=========================================%
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	213
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	214 % 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	215 % 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	216 % 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	217 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	218 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	219 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	220 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	221 % 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	222
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 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	224 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	225 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	226 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	227 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	228
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	229 % 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	230 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	231 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	232 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	233 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	234 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	235
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236 % 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	237 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	238 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	239 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	240 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	241 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	242 -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	243 -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	244 -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	245
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	246 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	247 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	248 +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	249 +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	250
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	251 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	252 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	253 end
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 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	257 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	258 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	259 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	260 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	261
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	262 % 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	263 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	264 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	265 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	266
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	267 % Misc.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	268 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	269 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	270 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	271 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	272 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	273
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	274 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	275
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	276
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	277 % 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	278 % 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	279 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	280 % type is a string specifying the type of boundary condition if there are several.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	281 % 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	282 % 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	283 % 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	284 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 default_arg('type','free');
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286 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	287
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	288 % 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	289 % 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	290 % 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	291 % 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	292 [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	293 switch nj
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	294 case 1
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	295 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	296 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	297 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	298 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	299 case -1
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	300 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	301 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	302 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	303 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	304 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	305
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	306 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	307 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	308 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	309 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	310 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	311 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	312
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	313 phi = obj.phi;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	314 H11 = obj.H11;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	315 h = obj.h;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	316 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	317 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	318
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	319 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	320 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	321
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	322 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	323 penalty = 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	324 switch type
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	325 % Dirichlet boundary condition
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	326 case {'D','d','dirichlet'}
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	327 error('not implemented')
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	328 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	329 phi = obj.phi;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	330
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	331 sigma = tuning * obj.dim/(H11*h(j)) +...
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	332 tuning * 1/(H11h(j)phi);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	333
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	334 closure = - sigmaE{j}RHOiHiAe{j}H_gammae{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	335 + njRHOi_kronHi_kronDiv'Ae{j}H_gammae{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	336
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	337 penalty = + sigmaE{j}RHOiHiAe{j}H_gamma ...
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	338 - njRHOi_kronHi_kronDiv'Ae{j}H_gamma;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	339
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	340 % Free boundary condition
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	341 case {'F','f','Free','free'}
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	342
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	343 % Loop over components of traction
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344 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	345 closure = closure - E{i}RHOiHie{j}H_gamma* (e{j}'*tau{i} );
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346 penalty{i} = E{i}RHOiHie{j}H_gamma;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	347 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	348
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	349
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350 % 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	351 otherwise
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352 error('No such boundary condition: type = %s',type);
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	353 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	354 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	355
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	356 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	357 % 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	358 % 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	359 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	360 % 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	361 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	362 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	363
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	364 % 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	365 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	366
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	367 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	368 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	369 j = 1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	370 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	371 j = 2;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	372 otherwise
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	373 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	374 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	375
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	376 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	377 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	378 nj = -1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	379 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	380 nj = 1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	381 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	382 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	384 % 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	385 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	386
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	387 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	388 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	389 j = 1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	390 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	391 j = 2;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	392 otherwise
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	393 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	394 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	395
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	396 switch op
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	397 case 'e'
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	398 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	399 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	400 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	401 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	402 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	403 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	404 case 'd'
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	405 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	406 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	407 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	408 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	409 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	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 otherwise
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	412 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	413 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	414
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
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	417 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	418 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	419 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	420 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	421 end

678

06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient.