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annotate +scheme/Heat2dVariable.m @ 1031:2ef20d00b386 feature/advectionRV

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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
parents 21394c78c72e
children 78db023a7fe3
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 classdef Heat2dVariable < scheme.Scheme
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2
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3 % Discretizes the Laplacian with variable coefficent,
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4 % In the Heat equation way (i.e., the discretization matrix is not necessarily
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5 % symmetric)
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6 % u_t = div * (kappa * grad u )
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7 % opSet should be cell array of opSets, one per dimension. This
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8 % is useful if we have periodic BC in one direction.
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9
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10 properties
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11 m % Number of points in each direction, possibly a vector
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12 h % Grid spacing
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13
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14 grid
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15 dim
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16
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17 order % Order of accuracy for the approximation
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18
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19 % Diagonal matrix for variable coefficients
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20 KAPPA % Variable coefficient
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21
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22 D % Total operator
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23 D1 % First derivatives
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24
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25 % Second derivatives
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26 D2_kappa
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27
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28 H, Hi % Inner products
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29 e_l, e_r
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30 d1_l, d1_r % Normal derivatives at the boundary
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31 alpha % Vector of borrowing constants
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32
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33 H_boundary % Boundary inner products
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34
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35 end
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36
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37 methods
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38
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39 function obj = Heat2dVariable(g ,order, kappa_fun, opSet)
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40 default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable});
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41 default_arg('kappa_fun', @(x,y) 0*x+1);
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42 dim = 2;
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43
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44 assert(isa(g, 'grid.Cartesian'))
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45
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46 kappa = grid.evalOn(g, kappa_fun);
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47 m = g.size();
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48 m_tot = g.N();
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49
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50 h = g.scaling();
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51 lim = g.lim;
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52
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53 % 1D operators
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54 ops = cell(dim,1);
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55 for i = 1:dim
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56 ops{i} = opSet{i}(m(i), lim{i}, order);
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57 end
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58
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59 I = cell(dim,1);
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60 D1 = cell(dim,1);
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61 D2 = cell(dim,1);
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62 H = cell(dim,1);
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63 Hi = cell(dim,1);
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64 e_l = cell(dim,1);
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65 e_r = cell(dim,1);
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66 d1_l = cell(dim,1);
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67 d1_r = cell(dim,1);
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68
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69 for i = 1:dim
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70 I{i} = speye(m(i));
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71 D1{i} = ops{i}.D1;
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72 D2{i} = ops{i}.D2;
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73 H{i} = ops{i}.H;
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74 Hi{i} = ops{i}.HI;
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75 e_l{i} = ops{i}.e_l;
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76 e_r{i} = ops{i}.e_r;
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77 d1_l{i} = ops{i}.d1_l;
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78 d1_r{i} = ops{i}.d1_r;
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79 end
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80
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81 %====== Assemble full operators ========
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82 KAPPA = spdiag(kappa);
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83 obj.KAPPA = KAPPA;
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84
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85 obj.D1 = cell(dim,1);
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86 obj.D2_kappa = cell(dim,1);
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87 obj.e_l = cell(dim,1);
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88 obj.e_r = cell(dim,1);
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89 obj.d1_l = cell(dim,1);
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90 obj.d1_r = cell(dim,1);
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91
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92 % D1
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93 obj.D1{1} = kron(D1{1},I{2});
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94 obj.D1{2} = kron(I{1},D1{2});
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95
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96 % Boundary operators
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97 obj.e_l{1} = kron(e_l{1},I{2});
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98 obj.e_l{2} = kron(I{1},e_l{2});
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99 obj.e_r{1} = kron(e_r{1},I{2});
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100 obj.e_r{2} = kron(I{1},e_r{2});
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101
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102 obj.d1_l{1} = kron(d1_l{1},I{2});
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103 obj.d1_l{2} = kron(I{1},d1_l{2});
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104 obj.d1_r{1} = kron(d1_r{1},I{2});
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105 obj.d1_r{2} = kron(I{1},d1_r{2});
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106
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107 % D2
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108 for i = 1:dim
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109 obj.D2_kappa{i} = sparse(m_tot);
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110 end
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111 ind = grid.funcToMatrix(g, 1:m_tot);
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112
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113 for i = 1:m(2)
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114 D_kappa = D2{1}(kappa(ind(:,i)));
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115 p = ind(:,i);
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116 obj.D2_kappa{1}(p,p) = D_kappa;
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117 end
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118
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119 for i = 1:m(1)
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120 D_kappa = D2{2}(kappa(ind(i,:)));
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121 p = ind(i,:);
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122 obj.D2_kappa{2}(p,p) = D_kappa;
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123 end
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124
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125 % Quadratures
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126 obj.H = kron(H{1},H{2});
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127 obj.Hi = inv(obj.H);
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128 obj.H_boundary = cell(dim,1);
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129 obj.H_boundary{1} = H{2};
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130 obj.H_boundary{2} = H{1};
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131
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132 % Differentiation matrix D (without SAT)
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133 D2_kappa = obj.D2_kappa;
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134 D1 = obj.D1;
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135 D = sparse(m_tot,m_tot);
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136 for i = 1:dim
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137 D = D + D2_kappa{i};
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138 end
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139 obj.D = D;
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140 %=========================================%
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141
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142 % Misc.
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143 obj.m = m;
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144 obj.h = h;
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145 obj.order = order;
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146 obj.grid = g;
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147 obj.dim = dim;
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148 obj.alpha = [ops{1}.borrowing.M.d1, ops{2}.borrowing.M.d1];
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149
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150 end
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151
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152
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153 % Closure functions return the operators applied to the own domain to close the boundary
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154 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
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parents:
diff changeset
155 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156 % type is a string specifying the type of boundary condition.
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 % data is a function returning the data that should be applied at the boundary.
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 % neighbour_scheme is an instance of Scheme that should be interfaced to.
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 % neighbour_boundary is a string specifying which boundary to interface to.
725
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
160 function [closure, penalty] = boundary_condition(obj, boundary, type, symmetric, tuning)
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
161 default_arg('type','Neumann');
725
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
162 default_arg('symmetric', false);
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
163 default_arg('tuning',1.2);
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
164
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165 % j is the coordinate direction of the boundary
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 % nj: outward unit normal component.
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167 % nj = -1 for west, south, bottom boundaries
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168 % nj = 1 for east, north, top boundaries
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169 [j, nj] = obj.get_boundary_number(boundary);
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
170 switch nj
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
171 case 1
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
172 e = obj.e_r;
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
173 d = obj.d1_r;
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174 case -1
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 e = obj.e_l;
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
176 d = obj.d1_l;
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
177 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
178
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
179 Hi = obj.Hi;
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
180 H_gamma = obj.H_boundary{j};
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
181 KAPPA = obj.KAPPA;
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
182 kappa_gamma = e{j}'*KAPPA*e{j};
725
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
183 h = obj.h(j);
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
184 alpha = h*obj.alpha(j);
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
185
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
186 switch type
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
187
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
188 % Dirichlet boundary condition
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
189 case {'D','d','dirichlet','Dirichlet'}
725
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
190
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
191 if ~symmetric
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192 closure = -nj*Hi*d{j}*kappa_gamma*H_gamma*(e{j}' );
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193 penalty = nj*Hi*d{j}*kappa_gamma*H_gamma;
725
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
194 else
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
195 closure = nj*Hi*d{j}*kappa_gamma*H_gamma*(e{j}' )...
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
196 -tuning*2/alpha*Hi*e{j}*kappa_gamma*H_gamma*(e{j}' ) ;
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
197 penalty = -nj*Hi*d{j}*kappa_gamma*H_gamma ...
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
198 +tuning*2/alpha*Hi*e{j}*kappa_gamma*H_gamma;
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
199 end
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201 % Free boundary condition
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 case {'N','n','neumann','Neumann'}
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203 closure = -nj*Hi*e{j}*kappa_gamma*H_gamma*(d{j}' );
724
a9e8c9d71307 Modify penalty for Neumann in Head2d so that data is for normal derivative and not u_x or u_y.
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
204 penalty = Hi*e{j}*kappa_gamma*H_gamma;
a9e8c9d71307 Modify penalty for Neumann in Head2d so that data is for normal derivative and not u_x or u_y.
Martin Almquist <malmquist@stanford.edu>
parents: 689
diff changeset
205 % penalty is for normal derivative and not for derivative, hence the sign.
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207 % Unknown boundary condition
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208 otherwise
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 error('No such boundary condition: type = %s',type);
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
210 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
212
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
213 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214 % u denotes the solution in the own domain
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 % v denotes the solution in the neighbour domain
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216 error('Interface not implemented');
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
218
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220 function [j, nj] = get_boundary_number(obj, boundary)
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
221
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
222 switch boundary
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224 j = 1;
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
226 j = 2;
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
227 otherwise
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
228 error('No such boundary: boundary = %s',boundary);
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
229 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
230
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
231 switch boundary
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
232 case {'w','W','west','West','s','S','south','South'}
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
233 nj = -1;
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
234 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
235 nj = 1;
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
236 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
237 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
238
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
239 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
240 function [return_op] = get_boundary_operator(obj, op, boundary)
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
241
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
242 switch boundary
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
243 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
244 j = 1;
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
245 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
246 j = 2;
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
247 otherwise
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
248 error('No such boundary: boundary = %s',boundary);
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
249 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
250
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251 switch op
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
252 case 'e'
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
253 switch boundary
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
254 case {'w','W','west','West','s','S','south','South'}
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
255 return_op = obj.e_l{j};
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
256 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
257 return_op = obj.e_r{j};
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
258 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
259 case 'd'
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
260 switch boundary
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
261 case {'w','W','west','West','s','S','south','South'}
689
60eb7f46d8d9 Bugfix get_boundary_op in Elastic2d and Heat2d
Martin Almquist <malmquist@stanford.edu>
parents: 688
diff changeset
262 return_op = obj.d1_l{j};
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
263 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
689
60eb7f46d8d9 Bugfix get_boundary_op in Elastic2d and Heat2d
Martin Almquist <malmquist@stanford.edu>
parents: 688
diff changeset
264 return_op = obj.d1_r{j};
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
265 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
266 otherwise
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
267 error(['No such operator: operatr = ' op]);
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
268 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
269
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
270 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
271
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
272 function N = size(obj)
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
273 N = prod(obj.m);
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
274 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
275 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
276 end