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annotate +scheme/Heat2dVariable.m @ 1198:2924b3a9b921 feature/d2_compatible

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Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
author Martin Almquist <malmquist@stanford.edu>
date Fri, 16 Aug 2019 14:30:28 -0700
parents 8d73fcdb07a5
children
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688
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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
688
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5 % symmetric)
997
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6 % u_t = div * (kappa * grad u )
688
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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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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
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.
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
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
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
165 % nj: outward unit normal component.
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 % nj = -1 for west, south, bottom boundaries
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167 % nj = 1 for east, north, top boundaries
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
168 nj = obj.getBoundarySign(boundary);
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
170 Hi = obj.Hi;
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
171 [e, d] = obj.getBoundaryOperator({'e', 'd'}, boundary);
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
172 H_gamma = obj.getBoundaryQuadrature(boundary);
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
173 alpha = obj.getBoundaryBorrowing(boundary);
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
174
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 KAPPA = obj.KAPPA;
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
176 kappa_gamma = e'*KAPPA*e;
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
177
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
178 switch type
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
179
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
180 % Dirichlet boundary condition
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
181 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
182
e9e15d64f9f9 Implement symmetric Dirichlet BC with variable tuning parameter in Heat2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 724
diff changeset
183 if ~symmetric
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
184 closure = -nj*Hi*d*kappa_gamma*H_gamma*(e' );
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
185 penalty = nj*Hi*d*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
186 else
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
187 closure = nj*Hi*d*kappa_gamma*H_gamma*(e' )...
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
188 -tuning*2/alpha*Hi*e*kappa_gamma*H_gamma*(e' ) ;
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
189 penalty = -nj*Hi*d*kappa_gamma*H_gamma ...
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
190 +tuning*2/alpha*Hi*e*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
191 end
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193 % Free boundary condition
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
194 case {'N','n','neumann','Neumann'}
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
195 closure = -nj*Hi*e*kappa_gamma*H_gamma*(d' );
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
196 penalty = Hi*e*kappa_gamma*H_gamma;
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
197 % 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
198
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
199 % Unknown boundary condition
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200 otherwise
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201 error('No such boundary condition: type = %s',type);
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 % u denotes the solution in the own domain
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207 % v denotes the solution in the neighbour domain
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208 error('Interface not implemented');
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
210
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
211 % Returns the boundary operator op for the boundary specified by the string boundary.
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
212 % op -- string or a cell array of strings
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
213 % boundary -- string
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
214 function varargout = getBoundaryOperator(obj, op, boundary)
1042
8d73fcdb07a5 Add asserts to boundary identifier inputs
Jonatan Werpers <jonatan@werpers.com>
parents: 997
diff changeset
215 assertIsMember(boundary, {'w', 'e', 's', 'n'})
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
217 if ~iscell(op)
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
218 op = {op};
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
221 for i = 1:numel(op)
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
222 switch op{i}
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
223 case 'e'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
224 switch boundary
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
225 case 'w'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
226 e = obj.e_l{1};
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
227 case 'e'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
228 e = obj.e_r{1};
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
229 case 's'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
230 e = obj.e_l{2};
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
231 case 'n'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
232 e = obj.e_r{2};
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
233 end
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
234 varargout{i} = e;
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
235
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
236 case 'd'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
237 switch boundary
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
238 case 'w'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
239 d = obj.d1_l{1};
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
240 case 'e'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
241 d = obj.d1_r{1};
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
242 case 's'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
243 d = obj.d1_l{2};
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
244 case 'n'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
245 d = obj.d1_r{2};
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
246 end
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
247 varargout{i} = d;
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
248 end
688
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 end
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
252 % Returns square boundary quadrature matrix, of dimension
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
253 % corresponding to the number of boundary points
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
254 %
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
255 % boundary -- string
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
256 function H_b = getBoundaryQuadrature(obj, boundary)
1042
8d73fcdb07a5 Add asserts to boundary identifier inputs
Jonatan Werpers <jonatan@werpers.com>
parents: 997
diff changeset
257 assertIsMember(boundary, {'w', 'e', 's', 'n'})
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
258
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
259 switch boundary
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
260 case 'w'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
261 H_b = obj.H_boundary{1};
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
262 case 'e'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
263 H_b = obj.H_boundary{1};
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
264 case 's'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
265 H_b = obj.H_boundary{2};
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
266 case 'n'
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
267 H_b = obj.H_boundary{2};
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
268 end
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
269 end
688
eb2f9233acc3 Add scheme Heat2dVariable
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
270
997
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
271 % Returns the boundary sign. The right boundary is considered the positive boundary
78db023a7fe3 Add getBoundaryOperator method to all 2d schemes, except obsolete Wave2dCurve and ElastiCurve, which needs a big makeover.
Martin Almquist <malmquist@stanford.edu>
parents: 943
diff changeset
272 % boundary -- string
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273 function s = getBoundarySign(obj, boundary)
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274 assertIsMember(boundary, {'w', 'e', 's', 'n'})
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275
997
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276 switch boundary
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277 case {'e','n'}
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278 s = 1;
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279 case {'w','s'}
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280 s = -1;
688
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281 end
997
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282 end
688
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283
997
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284 % Returns borrowing constant gamma*h
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285 % boundary -- string
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286 function gamm = getBoundaryBorrowing(obj, boundary)
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287 assertIsMember(boundary, {'w', 'e', 's', 'n'})
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288
997
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289 switch boundary
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290 case {'w','e'}
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291 gamm = obj.h(1)*obj.alpha(1);
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292 case {'s','n'}
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293 gamm = obj.h(2)*obj.alpha(2);
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294 end
688
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295 end
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296
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297 function N = size(obj)
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298 N = prod(obj.m);
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299 end
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300 end
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301 end