sbplib: +scheme/Elastic2dVariableAnisotropic.m annotate

annotate +scheme/Elastic2dVariableAnisotropic.m @ 1338:da61892884a4 feature/D2_boundary_opt

Add support for using periodic grids.

author	Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date	Fri, 13 May 2022 13:29:05 +0200
parents	8d9fc7981796
children

rev	line source
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	1 classdef Elastic2dVariableAnisotropic < scheme.Scheme
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	2
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	3 % Discretizes the elastic wave equation:
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	4 % rho u_{i,tt} = dj C_{ijkl} dk u_j
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	5 % opSet should be cell array of opSets, one per dimension. This
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	6 % is useful if we have periodic BC in one direction.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7 % Assumes fully compatible operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9 properties
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	10 m % Number of points in each direction, possibly a vector
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11 h % Grid spacing
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13 grid
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14 dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	15
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16 order % Order of accuracy for the approximation
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	18 % Diagonal matrices for variable coefficients
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19 RHO, RHOi, RHOi_kron % Density
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20 C % Elastic stiffness tensor
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22 D % Total operator
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	23 D1 % First derivatives
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	24 % D2 % Second derivatives
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 % Boundary operators in cell format, used for BC
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27 T_w, T_e, T_s, T_n
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29 % Traction operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	30 tau_w, tau_e, tau_s, tau_n % Return vector field
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	31 tau1_w, tau1_e, tau1_s, tau1_n % Return scalar field
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32 tau2_w, tau2_e, tau2_s, tau2_n % Return scalar field
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	33
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	34 % Inner products
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	35 H, Hi, Hi_kron, H_1D
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	36
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	37 % Boundary inner products (for scalar field)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	38 H_w, H_e, H_s, H_n
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	39
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	40 % Boundary restriction operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 e_w, e_e, e_s, e_n % Act on vector field, return vector field at boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42 e1_w, e1_e, e1_s, e1_n % Act on vector field, return scalar field at boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 e2_w, e2_e, e2_s, e2_n % Act on vector field, return scalar field at boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44 e_scalar_w, e_scalar_e, e_scalar_s, e_scalar_n; % Act on scalar field, return scalar field
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	45
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46 % E{i}^T picks out component i
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	47 E
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	48
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	49 % Borrowing constants of the form gamma*h, where gamma is a dimensionless constant.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	50 h11 % First entry in norm matrix
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	51
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	52 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54 methods
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56 % The coefficients can either be function handles or grid functions
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	57 % optFlag -- if true, extra computations are performed, which may be helpful for optimization.
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	58 function obj = Elastic2dVariableAnisotropic(g, order, rho, C, opSet, optFlag, hollow)
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	59 default_arg('hollow', false);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	60 default_arg('rho', @(x,y) 0*x+1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	61 default_arg('opSet',{@sbp.D2VariableCompatible, @sbp.D2VariableCompatible});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	62 default_arg('optFlag', false);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	63 dim = 2;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	64
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	65 C_default = cell(dim,dim,dim,dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	66 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	67 for j = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	68 for k = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	69 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	70 C_default{i,j,k,l} = @(x,y) 0*x + 1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	71 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	72 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	73 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	74 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	75 default_arg('C', C_default);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	76 assert(isa(g, 'grid.Cartesian'))
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	77
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	78 if isa(rho, 'function_handle')
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	79 rho = grid.evalOn(g, rho);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	80 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	82 C_mat = cell(dim,dim,dim,dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	83 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	84 for j = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	85 for k = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	86 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	87 if isa(C{i,j,k,l}, 'function_handle')
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	88 C{i,j,k,l} = grid.evalOn(g, C{i,j,k,l});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	89 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	90 C_mat{i,j,k,l} = spdiag(C{i,j,k,l});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	91 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	92 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	93 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	94 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	95 obj.C = C_mat;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	96
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	97 m = g.size();
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	98 m_tot = g.N();
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	99 lim = g.lim;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	100 if isempty(lim)
1338 da61892884a4 Add support for using periodic grids. Vidar Stiernström <vidar.stiernstrom@it.uu.se> parents: 1335 diff changeset	101 % TODO: Work for periodic grids (last gp not included)!
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	102 x = g.x;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	103 lim = cell(length(x),1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	104 for i = 1:length(x)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	105 lim{i} = {min(x{i}), max(x{i})};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	106 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	107 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	108
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	109 % 1D operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	110 ops = cell(dim,1);
1303 49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	111 opsHollow = cell(dim,1);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	112 h = zeros(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	113 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	114 ops{i} = opSet{i}(m(i), lim{i}, order);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	115 h(i) = ops{i}.h;
1303 49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	116 if hollow
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	117 opsHollow{i} = sbp.D2VariableCompatibleHollow(m(i), lim{i}, order);
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	118 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	119 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	120
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	121 % Borrowing constants
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	122 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	123 obj.h11{i} = h(i)*ops{i}.borrowing.H11;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	124 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	125
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	126 I = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	127 D1 = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	128 D2 = cell(dim,1);
1303 49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	129 D2Hollow = cell(dim,1);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	130 H = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	131 Hi = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	132 e_0 = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	133 e_m = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	134 d1_0 = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	135 d1_m = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	136
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	138 I{i} = speye(m(i));
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	139 D1{i} = ops{i}.D1;
1303 49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	140 if hollow
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	141 D2Hollow{i} = opsHollow{i}.D2;
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	142 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	143 D2{i} = ops{i}.D2;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	144 H{i} = ops{i}.H;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	145 Hi{i} = ops{i}.HI;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	146 e_0{i} = ops{i}.e_l;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	147 e_m{i} = ops{i}.e_r;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	148 d1_0{i} = ops{i}.d1_l;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	149 d1_m{i} = ops{i}.d1_r;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	150 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	151
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	152 %====== Assemble full operators ========
1206 6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	153 I_dim = speye(dim, dim);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	154 RHO = spdiag(rho);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	155 obj.RHO = RHO;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	156 obj.RHOi = inv(RHO);
1206 6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	157 obj.RHOi_kron = kron(obj.RHOi, I_dim);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	158
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	159 obj.D1 = cell(dim,1);
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	160 D2_temp = cell(dim,dim,dim);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	161
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	162 % D1
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	163 obj.D1{1} = kron(D1{1},I{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	164 obj.D1{2} = kron(I{1},D1{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	165
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	166 % Boundary restriction operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	167 e_l = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	168 e_r = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	169 e_l{1} = kron(e_0{1}, I{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	170 e_l{2} = kron(I{1}, e_0{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	171 e_r{1} = kron(e_m{1}, I{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	172 e_r{2} = kron(I{1}, e_m{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	173
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	174 e_scalar_w = e_l{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	175 e_scalar_e = e_r{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	176 e_scalar_s = e_l{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	177 e_scalar_n = e_r{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	179 e_w = kron(e_scalar_w, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	180 e_e = kron(e_scalar_e, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	181 e_s = kron(e_scalar_s, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	182 e_n = kron(e_scalar_n, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	183
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	184 % E{i}^T picks out component i.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	185 E = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	186 I = speye(m_tot,m_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	187 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	188 e = sparse(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	189 e(i) = 1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190 E{i} = kron(I,e);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	191 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	192 obj.E = E;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	193
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	194 e1_w = (e_scalar_w'*E{1}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	195 e1_e = (e_scalar_e'*E{1}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	196 e1_s = (e_scalar_s'*E{1}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	197 e1_n = (e_scalar_n'*E{1}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	198
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	199 e2_w = (e_scalar_w'*E{2}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	200 e2_e = (e_scalar_e'*E{2}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	201 e2_s = (e_scalar_s'*E{2}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	202 e2_n = (e_scalar_n'*E{2}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	203
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	204
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	205 % D2
1335 8d9fc7981796 Calculate width for all orders Vidar Stiernström <vidar.stiernstrom@it.uu.se> parents: 1304 diff changeset	206 width = order+1;
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	207 switch order
89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	208 case 2
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	209 nBP = 2;
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	210 case 4
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	211 nBP = 6;
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	212 case 6
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	213 nBP = 9;
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	214 end
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	215 for j = 1:dim
1206 6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	216 for k = 1:dim
6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	217 for l = 1:dim
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	218 if hollow
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	219 D2_temp{j,k,l} = sparse(m_tot, m_tot);
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	220 else
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	221 D2_temp{j,k,l} = spalloc(m_tot, m_tot, width*m_tot);
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	222 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	224 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	225 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	226 ind = grid.funcToMatrix(g, 1:m_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	227
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	228 k = 1;
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	229 if hollow
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	230 mask = sparse(m(1), m(1));
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	231 mask(1:nBP, 1:nBP) = speye(nBP, nBP);
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	232 mask(end-nBP+1:end, end-nBP+1:end) = speye(nBP, nBP);
1304 a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	233 maskXSmall = kron(mask, speye(m(2), m(2)));
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	234 maskX = E{1}maskXSmallE{1}' + E{2}maskXSmallE{2}';
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	235 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236 for r = 1:m(2)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	237 p = ind(:,r);
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	238 for j = 1:dim
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	239 for l = 1:dim
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	240 coeff = C{k,j,k,l};
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	241 if hollow && r > nBP && r < m(2) - nBP + 1
1303 49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	242 D_kk = D2Hollow{1}(coeff(p));
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	243 else
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	244 D_kk = D2{1}(coeff(p));
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	245 end
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	246 D2_temp{j,k,l}(p,p) = D_kk;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	247 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	248 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	249 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	250
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	251 k = 2;
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	252 if hollow
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	253 mask = sparse(m(2), m(2));
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	254 mask(1:nBP, 1:nBP) = speye(nBP, nBP);
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	255 mask(end-nBP+1:end, end-nBP+1:end) = speye(nBP, nBP);
1304 a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	256 maskYSmall = kron(speye(m(1), m(1)), mask);
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	257
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	258 maskY = E{1}maskYSmallE{1}' + E{2}maskYSmallE{2}';
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	259 mask = maskX + maskY;
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	260 mask = mask>0;
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	261
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	262 maskSmall = maskXSmall + maskYSmall;
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	263 maskSmall = maskSmall>0;
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	264 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	265 for r = 1:m(1)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	266 p = ind(r,:);
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	267 for j = 1:dim
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	268 for l = 1:dim
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	269 coeff = C{k,j,k,l};
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	270 if hollow && r > nBP && r < m(1) - nBP + 1
1303 49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	271 D_kk = D2Hollow{2}(coeff(p));
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	272 else
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	273 D_kk = D2{2}(coeff(p));
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	274 end
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	275 D2_temp{j,k,l}(p,p) = D_kk;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	276 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	277 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	278 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	279
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	280 % Quadratures
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	281 obj.H = kron(H{1},H{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	282 obj.Hi = inv(obj.H);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	283 obj.H_w = H{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	284 obj.H_e = H{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 obj.H_s = H{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286 obj.H_n = H{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	287 obj.H_1D = {H{1}, H{2}};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	288
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	289 % Differentiation matrix D (without SAT)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	290 D1 = obj.D1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	291 D = sparse(dimm_tot,dimm_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	292 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	293 for j = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	294 for k = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	295 for l = 1:dim
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	296 if i == k
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	297 D = D + E{j}D2_temp{j,k,l}E{l}';
89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	298 D2_temp{j,k,l} = [];
1206 6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	299 else
1304 a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	300 if hollow
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	301 D = D + E{j}(maskSmallD1{i})C_mat{i,j,k,l}D1{k}*E{l}';
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	302 else
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	303 D = D + E{j}(D1{i})C_mat{i,j,k,l}D1{k}E{l}';
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	304 end
1206 6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	305 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	306 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	307 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	308 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	309 end
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	310 clear D2_temp;
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	311 if hollow
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	312 mask = maskX + maskY;
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	313 mask = mask>0;
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	314 D = mask*D;
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	315 end
1206 6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	316 D = obj.RHOi_kron*D;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	317 obj.D = D;
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	318 clear D;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	319 %=========================================%'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	320
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	321 % Numerical traction operators for BC.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	322 %
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	323 % Formula at boundary j: % tau^{j}_i = sum_l T^{j}_{il} u_l
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	324 %
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	325 T_l = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	326 T_r = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	327 tau_l = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	328 tau_r = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	329
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	330 D1 = obj.D1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	331
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	332 % Boundary j
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	333 for j = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	334 T_l{j} = cell(dim,dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	335 T_r{j} = cell(dim,dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	336 tau_l{j} = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	337 tau_r{j} = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	338
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	339 [~, n_l] = size(e_l{j});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	340 [~, n_r] = size(e_r{j});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	341
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	342 % Traction component i
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	343 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344 tau_l{j}{i} = sparse(dim*m_tot, n_l);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	345 tau_r{j}{i} = sparse(dim*m_tot, n_r);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	347 % Displacement component l
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	348 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	349 T_l{j}{i,l} = sparse(m_tot, n_l);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350 T_r{j}{i,l} = sparse(m_tot, n_r);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	351
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352 % Derivative direction k
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	353 for k = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	354 T_l{j}{i,l} = T_l{j}{i,l} ...
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	355 - (e_l{j}'C_mat{j,i,k,l}D1{k})';
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	356 T_r{j}{i,l} = T_r{j}{i,l} ...
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	357 + (e_r{j}'C_mat{j,i,k,l}D1{k})';
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	358 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	359 tau_l{j}{i} = tau_l{j}{i} + (T_l{j}{i,l}'*E{l}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	360 tau_r{j}{i} = tau_r{j}{i} + (T_r{j}{i,l}'*E{l}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	361 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	362 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	363 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	364
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	365 % Traction tensors, T_ij
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	366 obj.T_w = T_l{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	367 obj.T_e = T_r{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	368 obj.T_s = T_l{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	369 obj.T_n = T_r{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	370
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	371 % Restriction operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	372 obj.e_w = e_w;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	373 obj.e_e = e_e;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	374 obj.e_s = e_s;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	375 obj.e_n = e_n;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	376
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	377 obj.e1_w = e1_w;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	378 obj.e1_e = e1_e;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	379 obj.e1_s = e1_s;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	380 obj.e1_n = e1_n;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	381
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	382 obj.e2_w = e2_w;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383 obj.e2_e = e2_e;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	384 obj.e2_s = e2_s;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	385 obj.e2_n = e2_n;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	386
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	387 obj.e_scalar_w = e_scalar_w;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	388 obj.e_scalar_e = e_scalar_e;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	389 obj.e_scalar_s = e_scalar_s;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	390 obj.e_scalar_n = e_scalar_n;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	391
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	392 % First component of traction
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	393 obj.tau1_w = tau_l{1}{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	394 obj.tau1_e = tau_r{1}{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	395 obj.tau1_s = tau_l{2}{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	396 obj.tau1_n = tau_r{2}{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	397
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	398 % Second component of traction
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	399 obj.tau2_w = tau_l{1}{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	400 obj.tau2_e = tau_r{1}{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	401 obj.tau2_s = tau_l{2}{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	402 obj.tau2_n = tau_r{2}{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	403
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	404 % Traction vectors
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	405 obj.tau_w = (e_w'e1_wobj.tau1_w')' + (e_w'e2_wobj.tau2_w')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	406 obj.tau_e = (e_e'e1_eobj.tau1_e')' + (e_e'e2_eobj.tau2_e')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	407 obj.tau_s = (e_s'e1_sobj.tau1_s')' + (e_s'e2_sobj.tau2_s')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	408 obj.tau_n = (e_n'e1_nobj.tau1_n')' + (e_n'e2_nobj.tau2_n')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	409
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	410 % Kroneckered norms and coefficients
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	411 obj.Hi_kron = kron(obj.Hi, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	412
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	413 % Misc.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	414 obj.m = m;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	415 obj.h = h;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	416 obj.order = order;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	417 obj.grid = g;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	418 obj.dim = dim;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	419
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	420 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	421
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	422
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	423 % Closure functions return the operators applied to the own domain to close the boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	424 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	425 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	426 % bc is a cell array of component and bc type, e.g. {1, 'd'} for Dirichlet condition
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	427 % on the first component. Can also be e.g.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	428 % {'normal', 'd'} or {'tangential', 't'} for conditions on
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	429 % tangential/normal component.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	430 % data is a function returning the data that should be applied at the boundary.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	431 % neighbour_scheme is an instance of Scheme that should be interfaced to.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	432 % neighbour_boundary is a string specifying which boundary to interface to.
1203 25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	433
25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	434 % For displacement bc:
25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	435 % bc = {comp, 'd', dComps},
25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	436 % where
25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	437 % dComps = vector of components with displacement BC. Default: 1:dim.
25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	438 % In this way, we can specify one BC at a time even though the SATs depend on all BC.
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	439 function [closure, penalty] = boundary_condition(obj, boundary, bc, tuning)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	440 default_arg('tuning', 1.0);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	441
1202 31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	442 assert( iscell(bc), 'The BC type must be a 2x1 or 3x1 cell array' );
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	443 comp = bc{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	444 type = bc{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	445 if ischar(comp)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	446 comp = obj.getComponent(comp, boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	447 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	448
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	449 e = obj.getBoundaryOperatorForScalarField('e', boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	450 tau = obj.getBoundaryOperator(['tau' num2str(comp)], boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	451 T = obj.getBoundaryTractionOperator(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	452 h11 = obj.getBorrowing(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	453 H_gamma = obj.getBoundaryQuadratureForScalarField(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	454 nu = obj.getNormal(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	455
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	456 E = obj.E;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	457 Hi = obj.Hi;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	458 RHOi = obj.RHOi;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	459 C = obj.C;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	460
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	461 dim = obj.dim;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	462 m_tot = obj.grid.N();
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	463
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	464 % Preallocate
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	465 [~, col] = size(tau);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	466 closure = sparse(dimm_tot, dimm_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	467 penalty = sparse(dim*m_tot, col);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	468
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	469 j = comp;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	470 switch type
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	471
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	472 % Dirichlet boundary condition
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	473 case {'D','d','dirichlet','Dirichlet','displacement','Displacement'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	474
1202 31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	475 if numel(bc) >= 3
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	476 dComps = bc{3};
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	477 else
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	478 dComps = 1:dim;
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	479 end
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	480
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	481 % Loops over components that Dirichlet penalties end up on
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	482 % Y: symmetrizing part of penalty
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	483 % Z: symmetric part of penalty
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	484 % X = Y + Z.
1202 31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	485
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	486 % Nonsymmetric part goes on all components to
1203 25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	487 % yield traction in discrete energy rate
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	488 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	489 Y = T{j,i}';
1202 31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	490 X = e*Y;
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	491 closure = closure + E{i}RHOiHiX'eH_gamma(e'*E{j}' );
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	492 penalty = penalty - E{i}RHOiHiX'e*H_gamma;
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	493 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	494
1203 25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	495 % Symmetric part only required on components with displacement BC.
25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	496 % (Otherwise it's not symmetric.)
1202 31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	497 for i = dComps
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	498 Z = sparse(m_tot, m_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	499 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	500 for k = 1:dim
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	501 Z = Z + nu(l)C{l,i,k,j}nu(k);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	502 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	503 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	504 Z = -tuningdim/h11Z;
1202 31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	505 X = Z;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	506 closure = closure + E{i}RHOiHiX'eH_gamma(e'*E{j}' );
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	507 penalty = penalty - E{i}RHOiHiX'e*H_gamma;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	508 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	509
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	510 % Free boundary condition
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	511 case {'F','f','Free','free','traction','Traction','t','T'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	512 closure = closure - E{j}RHOiHieH_gamma*tau';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	513 penalty = penalty + E{j}RHOiHieH_gamma;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	514
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	515 % Unknown boundary condition
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	516 otherwise
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	517 error('No such boundary condition: type = %s',type);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	518 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	519 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	520
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	521 % type Struct that specifies the interface coupling.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	522 % Fields:
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	523 % -- tuning: penalty strength, defaults to 1.0
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	524 % -- interpolation: type of interpolation, default 'none'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	525 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	526
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	527 defaultType.tuning = 1.0;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	528 defaultType.interpolation = 'none';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	529 default_struct('type', defaultType);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	530
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	531 switch type.interpolation
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	532 case {'none', ''}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	533 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	534 case {'op','OP'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	535 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	536 otherwise
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	537 error('Unknown type of interpolation: %s ', type.interpolation);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	538 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	539 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	540
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	541 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	542 tuning = type.tuning;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	543
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	544 % u denotes the solution in the own domain
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	545 % v denotes the solution in the neighbour domain
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	546
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	547 u = obj;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	548 v = neighbour_scheme;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	549
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	550 % Operators, u side
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	551 e_u = u.getBoundaryOperatorForScalarField('e', boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	552 tau_u = u.getBoundaryOperator('tau', boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	553 h11_u = u.getBorrowing(boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	554 nu_u = u.getNormal(boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	555
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	556 E_u = u.E;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	557 C_u = u.C;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	558 m_tot_u = u.grid.N();
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	559
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	560 % Operators, v side
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	561 e_v = v.getBoundaryOperatorForScalarField('e', neighbour_boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	562 tau_v = v.getBoundaryOperator('tau', neighbour_boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	563 h11_v = v.getBorrowing(neighbour_boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	564 nu_v = v.getNormal(neighbour_boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	565
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	566 E_v = v.E;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	567 C_v = v.C;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	568 m_tot_v = v.grid.N();
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	569
1252 8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	570 % Fix {'e', 's'}, {'w', 'n'}, and {'x','x'} couplings
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	571 flipFlag = false;
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	572 e_v_flip = e_v;
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	573 if (strcmp(boundary,'s') && strcmp(neighbour_boundary,'e')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	574 (strcmp(boundary,'e') && strcmp(neighbour_boundary,'s')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	575 (strcmp(boundary,'w') && strcmp(neighbour_boundary,'n')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	576 (strcmp(boundary,'n') && strcmp(neighbour_boundary,'w')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	577 (strcmp(boundary,'s') && strcmp(neighbour_boundary,'s')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	578 (strcmp(boundary,'n') && strcmp(neighbour_boundary,'n')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	579 (strcmp(boundary,'w') && strcmp(neighbour_boundary,'w')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	580 (strcmp(boundary,'e') && strcmp(neighbour_boundary,'e'))
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	581
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	582 flipFlag = true;
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	583 e_v_flip = fliplr(e_v);
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	584
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	585 t1 = tau_v(:,1:2:end-1);
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	586 t2 = tau_v(:,2:2:end);
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	587
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	588 t1 = fliplr(t1);
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	589 t2 = fliplr(t2);
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	590
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	591 tau_v(:,1:2:end-1) = t1;
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	592 tau_v(:,2:2:end) = t2;
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	593 end
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	594
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	595 % Operators that are only required for own domain
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	596 Hi = u.Hi_kron;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	597 RHOi = u.RHOi_kron;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	598 e_kron = u.getBoundaryOperator('e', boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	599 T_u = u.getBoundaryTractionOperator(boundary);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	600
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	601 % Shared operators
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	602 H_gamma = u.getBoundaryQuadratureForScalarField(boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	603 H_gamma_kron = u.getBoundaryQuadrature(boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	604 dim = u.dim;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	605
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	606 % Preallocate
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	607 [~, m_int] = size(H_gamma);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	608 closure = sparse(dimm_tot_u, dimm_tot_u);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	609 penalty = sparse(dimm_tot_u, dimm_tot_v);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	610
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	611 % ---- Continuity of displacement ------
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	612
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	613 % Y: symmetrizing part of penalty
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	614 % Z: symmetric part of penalty
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	615 % X = Y + Z.
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	616
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	617 % Loop over components to couple across interface
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	618 for j = 1:dim
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	619
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	620 % Loop over components that penalties end up on
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	621 for i = 1:dim
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	622 Y = 1/2*T_u{j,i}';
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	623 Z_u = sparse(m_int, m_int);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	624 Z_v = sparse(m_int, m_int);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	625 for l = 1:dim
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	626 for k = 1:dim
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	627 Z_u = Z_u + e_u'nu_u(l)C_u{l,i,k,j}nu_u(k)e_u;
05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	628 Z_v = Z_v + e_v'nu_v(l)C_v{l,i,k,j}nu_v(k)e_v;
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	629 end
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	630 end
1252 8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	631
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	632 if flipFlag
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	633 Z_v = rot90(Z_v,2);
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	634 end
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	635
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	636 Z = -tuningdim( 1/(4h11_u)Z_u + 1/(4h11_v)Z_v );
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	637 X = Y + Z*e_u';
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	638 closure = closure + E_u{i}X'H_gammae_u'E_u{j}';
1252 8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	639 penalty = penalty - E_u{i}X'H_gammae_v_flip'E_v{j}';
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	640
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	641 end
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	642 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	643
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	644 % ---- Continuity of traction ------
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	645 closure = closure - 1/2e_kronH_gamma_kron*tau_u';
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	646 penalty = penalty - 1/2e_kronH_gamma_kron*tau_v';
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	647
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	648 % ---- Multiply by inverse of density x quadraure ----
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	649 closure = RHOiHiclosure;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	650 penalty = RHOiHipenalty;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	651
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	652 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	653
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	654 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	655 error('Non-conforming interfaces not implemented yet.');
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	656 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	657
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	658 % Returns the component number that is the tangential/normal component
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	659 % at the specified boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	660 function comp = getComponent(obj, comp_str, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	661 assertIsMember(comp_str, {'normal', 'tangential'});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	662 assertIsMember(boundary, {'w', 'e', 's', 'n'});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	663
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	664 switch boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	665 case {'w', 'e'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	666 switch comp_str
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	667 case 'normal'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	668 comp = 1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	669 case 'tangential'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	670 comp = 2;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	671 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	672 case {'s', 'n'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	673 switch comp_str
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	674 case 'normal'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	675 comp = 2;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	676 case 'tangential'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	677 comp = 1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	678 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	679 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	680 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	681
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	682 % Returns h11 for the boundary specified by the string boundary.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	683 % op -- string
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	684 function h11 = getBorrowing(obj, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	685 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	686
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	687 switch boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	688 case {'w','e'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	689 h11 = obj.h11{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	690 case {'s', 'n'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	691 h11 = obj.h11{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	692 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	693 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	694
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	695 % Returns the outward unit normal vector for the boundary specified by the string boundary.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	696 function nu = getNormal(obj, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	697 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	698
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	699 switch boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	700 case 'w'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	701 nu = [-1,0];
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	702 case 'e'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	703 nu = [1,0];
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	704 case 's'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	705 nu = [0,-1];
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	706 case 'n'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	707 nu = [0,1];
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	708 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	709 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	710
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	711 % Returns the boundary operator op for the boundary specified by the string boundary.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	712 % op -- string
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	713 function o = getBoundaryOperator(obj, op, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	714 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	715 assertIsMember(op, {'e', 'e1', 'e2', 'tau', 'tau1', 'tau2'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	716
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	717 switch op
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	718 case {'e', 'e1', 'e2', 'tau', 'tau1', 'tau2'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	719 o = obj.([op, '_', boundary]);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	720 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	721
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	722 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	723
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	724 % Returns the boundary operator op for the boundary specified by the string boundary.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	725 % op -- string
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	726 function o = getBoundaryOperatorForScalarField(obj, op, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	727 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	728 assertIsMember(op, {'e'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	729
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	730 switch op
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	731
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	732 case 'e'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	733 o = obj.(['e_scalar', '_', boundary]);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	734 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	735
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	736 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	737
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	738 % Returns the boundary operator T_ij (cell format) for the boundary specified by the string boundary.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	739 % Formula: tau_i = T_ij u_j
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	740 % op -- string
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	741 function T = getBoundaryTractionOperator(obj, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	742 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	743
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	744 T = obj.(['T', '_', boundary]);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	745 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	746
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	747 % Returns square boundary quadrature matrix, of dimension
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	748 % corresponding to the number of boundary unknowns
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	749 %
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	750 % boundary -- string
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	751 function H = getBoundaryQuadrature(obj, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	752 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	753
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	754 H = obj.getBoundaryQuadratureForScalarField(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	755 I_dim = speye(obj.dim, obj.dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	756 H = kron(H, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	757 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	758
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	759 % Returns square boundary quadrature matrix, of dimension
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	760 % corresponding to the number of boundary grid points
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	761 %
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	762 % boundary -- string
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	763 function H_b = getBoundaryQuadratureForScalarField(obj, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	764 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	765
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	766 H_b = obj.(['H_', boundary]);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	767 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	768
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	769 function N = size(obj)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	770 N = obj.dim*prod(obj.m);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	771 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	772 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	773 end

Mercurial > repos > public > sbplib

annotate +scheme/Elastic2dVariableAnisotropic.m @ 1338:da61892884a4 feature/D2_boundary_opt