sbplib: +scheme/elasticVariable.m annotate

annotate +scheme/elasticVariable.m @ 685:b035902869a8 feature/poroelastic

Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim.

author	Martin Almquist <malmquist@stanford.edu>
date	Thu, 08 Feb 2018 16:43:43 -0800
parents	247b58a4dbe8
children

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
685 b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	5 % opSet should be cell array of opSets, one per dimension. This
b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	6 % is useful if we have periodic BC in one direction.
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8 properties
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9 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	10 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	11
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12 grid
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13 dim
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 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	16
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17 % 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	18 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	19 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	20 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	21
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22 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	23 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	24
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25 % Second derivatives
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 D2_lambda
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27 D2_mu
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29 % 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	30 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	31 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	32
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	33 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	34 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	35 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	36 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	37 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	38 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	39 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	40
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 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	42
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 % 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	44 RHOi_kron
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	45 Hi_kron
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46 end
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 methods
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	49
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	50 function obj = elasticVariable(g ,order, lambda_fun, mu_fun, rho_fun, opSet)
685 b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	51 default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable});
678 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('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	53 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	54 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	55 dim = 2;
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 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	58
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	59 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	60 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	61 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	62 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	63 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	64
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	65 h = g.scaling();
685 b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	66 lim = g.lim;
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	67
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	68 % 1D operators
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	69 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	70 for i = 1:dim
685 b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	71 ops{i} = opSet{i}(m(i), lim{i}, order);
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	72 end
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 % Borrowing constants
685 b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	75 for i = 1:dim
b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	76 beta = ops{i}.borrowing.R.delta_D;
b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	77 obj.H11{i} = ops{i}.borrowing.H11;
b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	78 obj.phi{i} = beta/obj.H11{i};
b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	79 obj.gamma{i} = ops{i}.borrowing.M.d1;
b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	80 end
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	82 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	83 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	84 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	85 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	86 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	87 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	88 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	89 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	90 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	91
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	92 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	93 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	94 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	95 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	96 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	97 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	98 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	99 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	100 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	101 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	102 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	103
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	104 %====== 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	105 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	106 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	107 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	108 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	109 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	110 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	111 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	112
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	113 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	114 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	115 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	116 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	117 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	118 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	119 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	120
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	121 % D1
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{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	123 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	124
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	125 % Boundary operators
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	126 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	127 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	128 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	129 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	130
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	131 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	132 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	133 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	134 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	135
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	136 % D2
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137 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	138 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	139 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	140 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	141 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	142
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	143 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	144 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	145 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	146
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	147 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	148 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	149 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	150 end
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 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	153 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	154 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	155
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	156 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	157 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	158 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	159 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	160
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	161 % Quadratures
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 = 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	163 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	164 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	165 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	166 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	167
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	168 % 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	169 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	170 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	171 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	172 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	173 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	174 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	175 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	176 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	177
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178 % 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	179 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	180 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	181 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	182 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	183 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	184 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	185 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	186 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	187 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	188 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	189 );
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190 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	191 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	192 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	193 );
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	194 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	195 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	196 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	197 %=========================================%
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	198
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	199 % 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	200 % 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	201 % 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	202 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	203 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	204 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	205 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	206 % 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	207
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	208 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	209 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	210 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	211 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	212 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	213
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	214 % 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	215 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	216 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	217 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	218 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	219 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	220
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	221 % 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	222 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	223 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	224 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	225 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	226 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	227 -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	228 -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	229 -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	230
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	231 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	232 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	233 +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	234 +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	235
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236 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	237 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	238 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	239
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	240 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	241 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	242 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	243 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	244 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	245 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	246
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	247 % 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	248 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	249 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	250 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	251
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	252 % Misc.
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	253 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	254 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	255 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	256 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	257 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	258
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	259 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	260
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 % 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	263 % 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	264 % 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	265 % 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	266 % 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	267 % 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	268 % 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	269 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	270 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	271 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	272
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	273 % 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	274 % 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	275 % 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	276 % 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	277 [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	278 switch nj
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	279 case 1
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	280 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	281 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	282 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	283 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	284 case -1
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 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	286 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	287 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	288 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	289 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	290
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	291 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	292 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	293 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	294 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	295 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	296 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	297
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	298 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	299 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	300
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	301 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	302 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	303
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	304 % Preallocate
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	305 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	306 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	307 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	308 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	309 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	310
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	311 % 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	312 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	313 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	314
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	315 % 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	316 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	317
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	318 tuning = 1.2;
685 b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	319 phi = obj.phi{j};
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 h = obj.h(j);
685 b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	321 h11 = obj.H11{j}*h;
b035902869a8 Make scheme/elasticVariable work with different opSets in different dim to facilitate periodic in some dim. Martin Almquist <malmquist@stanford.edu> parents: 679 diff changeset	322 gamma = obj.gamma{j};
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 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	325 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	326 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	327
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	328 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	329 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	330 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	331 + 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	332 + 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	333
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	334 % 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	335 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	336 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	337 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	338 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	339 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	340 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	341 end
678 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 % 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	344 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	345 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	346 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	347
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	348 % 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	349 otherwise
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350 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	351 end
678 06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352 end
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
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	355 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	356 % 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	357 % 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	358 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	359 % 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	360 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	361 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	362
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	363 % 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	364 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	365
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	366 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	367 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	368 j = 1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	369 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	370 j = 2;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	371 otherwise
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	372 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	373 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	374
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	375 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	376 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	377 nj = -1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	378 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	379 nj = 1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	380 end
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
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383 % 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	384 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	385
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	386 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	387 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	388 j = 1;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	389 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	390 j = 2;
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	391 otherwise
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	392 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	393 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	394
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	395 switch op
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'
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	397 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	398 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	399 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	400 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	401 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	402 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	403 case 'd'
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	404 switch boundary
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	405 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	406 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	407 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	408 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	409 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	410 otherwise
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	411 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	412 end
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	413
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
06676c40e77f Add scheme for complete elastic operator. Traction BC working with MMS variable coefficient. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	416 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	417 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	418 end
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

Mercurial > repos > public > sbplib

annotate +scheme/elasticVariable.m @ 685:b035902869a8 feature/poroelastic