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annotate +scheme/Schrodinger2d.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 3dd7f87c9a1b
children 78db023a7fe3
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
718
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1 classdef Schrodinger2d < scheme.Scheme
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2
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3 % Discretizes the Laplacian with constant coefficent,
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
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4 % in the Schrödinger equation way (i.e., the discretization matrix is not necessarily
718
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5 % definite)
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6 % u_t = a*i*Laplace u
718
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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 a % Constant 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
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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 e_w, e_e, e_s, e_n
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32 d_w, d_e, d_s, d_n
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33
718
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34 H_boundary % Boundary inner products
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35
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36 end
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37
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38 methods
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39
912
1cdf5ead2a16 Refactor interface method for Schrodinger2d
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40 function obj = Schrodinger2d(g ,order, a, opSet)
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41 default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable});
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42 default_arg('a',1);
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43 dim = 2;
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44
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3dd7f87c9a1b Use assertType(...) instead of assert(isa(...))
Jonatan Werpers <jonatan@werpers.com>
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45 assertType(g, 'grid.Cartesian');
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46 if isa(a, 'function_handle')
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47 a = grid.evalOn(g, a);
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48 a = spdiag(a);
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49 end
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50
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51 m = g.size();
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52 m_tot = g.N();
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53
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54 h = g.scaling();
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55 xlim = {g.x{1}(1), g.x{1}(end)};
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56 ylim = {g.x{2}(1), g.x{2}(end)};
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57 lim = {xlim, ylim};
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58
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59 % 1D operators
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60 ops = cell(dim,1);
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61 for i = 1:dim
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62 ops{i} = opSet{i}(m(i), lim{i}, order);
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63 end
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64
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65 I = cell(dim,1);
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66 D1 = cell(dim,1);
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67 D2 = cell(dim,1);
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68 H = cell(dim,1);
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69 Hi = cell(dim,1);
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70 e_l = cell(dim,1);
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71 e_r = cell(dim,1);
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72 d1_l = cell(dim,1);
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73 d1_r = cell(dim,1);
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74
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75 for i = 1:dim
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76 I{i} = speye(m(i));
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77 D1{i} = ops{i}.D1;
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78 D2{i} = ops{i}.D2;
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79 H{i} = ops{i}.H;
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80 Hi{i} = ops{i}.HI;
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81 e_l{i} = ops{i}.e_l;
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82 e_r{i} = ops{i}.e_r;
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83 d1_l{i} = ops{i}.d1_l;
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84 d1_r{i} = ops{i}.d1_r;
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85 end
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86
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87 % Constant coeff D2
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88 for i = 1:dim
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89 D2{i} = D2{i}(ones(m(i),1));
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90 end
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91
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92 %====== Assemble full operators ========
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93 obj.D1 = cell(dim,1);
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94 obj.D2 = cell(dim,1);
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95 obj.e_l = cell(dim,1);
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96 obj.e_r = cell(dim,1);
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97 obj.d1_l = cell(dim,1);
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98 obj.d1_r = cell(dim,1);
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99
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100 % D1
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101 obj.D1{1} = kron(D1{1},I{2});
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102 obj.D1{2} = kron(I{1},D1{2});
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103
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104 % Boundary operators
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105 obj.e_l{1} = kron(e_l{1},I{2});
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106 obj.e_l{2} = kron(I{1},e_l{2});
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107 obj.e_r{1} = kron(e_r{1},I{2});
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108 obj.e_r{2} = kron(I{1},e_r{2});
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109
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110 obj.d1_l{1} = kron(d1_l{1},I{2});
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111 obj.d1_l{2} = kron(I{1},d1_l{2});
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112 obj.d1_r{1} = kron(d1_r{1},I{2});
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113 obj.d1_r{2} = kron(I{1},d1_r{2});
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114
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115 % D2
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116 obj.D2{1} = kron(D2{1},I{2});
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117 obj.D2{2} = kron(I{1},D2{2});
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118
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119 % Quadratures
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120 obj.H = kron(H{1},H{2});
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121 obj.Hi = inv(obj.H);
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122 obj.H_boundary = cell(dim,1);
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123 obj.H_boundary{1} = H{2};
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124 obj.H_boundary{2} = H{1};
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125
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126 % Differentiation matrix D (without SAT)
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127 D2 = obj.D2;
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128 D = sparse(m_tot,m_tot);
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
129 for j = 1:dim
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
130 D = D + a*1i*D2{j};
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parents:
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131 end
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
132 obj.D = D;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
133 %=========================================%
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134
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
135 % Misc.
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
136 obj.m = m;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
137 obj.h = h;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
138 obj.order = order;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
139 obj.grid = g;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
140 obj.dim = dim;
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Martin Almquist <malmquist@stanford.edu>
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141 obj.a = a;
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Martin Almquist <malmquist@stanford.edu>
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142 obj.e_w = obj.e_l{1};
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Martin Almquist <malmquist@stanford.edu>
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143 obj.e_e = obj.e_r{1};
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
144 obj.e_s = obj.e_l{2};
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Martin Almquist <malmquist@stanford.edu>
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145 obj.e_n = obj.e_r{2};
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Martin Almquist <malmquist@stanford.edu>
parents: 718
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146 obj.d_w = obj.d1_l{1};
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Martin Almquist <malmquist@stanford.edu>
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147 obj.d_e = obj.d1_r{1};
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148 obj.d_s = obj.d1_l{2};
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149 obj.d_n = obj.d1_r{2};
718
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150
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151 end
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152
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153
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154 % Closure functions return the operators applied to the own domain to close the boundary
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155 % 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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156 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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157 % type is a string specifying the type of boundary condition.
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158 % data is a function returning the data that should be applied at the boundary.
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159 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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160 % neighbour_boundary is a string specifying which boundary to interface to.
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parents:
diff changeset
161 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
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diff changeset
162 default_arg('type','Neumann');
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
163 default_arg('parameter', []);
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
164
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165 % j is the coordinate direction of the boundary
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
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166 % nj: outward unit normal component.
718
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167 % nj = -1 for west, south, bottom boundaries
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parents:
diff changeset
168 % nj = 1 for east, north, top boundaries
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diff changeset
169 [j, nj] = obj.get_boundary_number(boundary);
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diff changeset
170 switch nj
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
171 case 1
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
172 e = obj.e_r;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
173 d = obj.d1_r;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174 case -1
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 e = obj.e_l;
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
176 d = obj.d1_l;
71aa5828cbbf Add Schrödinger scheme for 2d single block. Will develop to multiblock with interpolation.
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parents:
diff changeset
177 end
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diff changeset
178
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
179 Hi = obj.Hi;
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diff changeset
180 H_gamma = obj.H_boundary{j};
743
f4595f14d696 Change schemes to work for special coefficients.
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parents: 719
diff changeset
181 a = e{j}'*obj.a*e{j};
718
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diff changeset
182
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
183 switch type
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184
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
185 % Dirichlet boundary condition
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parents:
diff changeset
186 case {'D','d','dirichlet','Dirichlet'}
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
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187 closure = nj*Hi*d{j}*a*1i*H_gamma*(e{j}' );
718
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188 penalty = -nj*Hi*d{j}*a*1i*H_gamma;
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189
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
190 % Free boundary condition
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
191 case {'N','n','neumann','Neumann'}
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
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192 closure = -nj*Hi*e{j}*a*1i*H_gamma*(d{j}' );
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193 penalty = nj*Hi*e{j}*a*1i*H_gamma;
718
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194
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Martin Almquist <malmquist@stanford.edu>
parents:
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195 % Unknown boundary condition
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Martin Almquist <malmquist@stanford.edu>
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196 otherwise
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parents:
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197 error('No such boundary condition: type = %s',type);
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diff changeset
198 end
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199 end
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200
939
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
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parents: 912
diff changeset
201 % type Struct that specifies the interface coupling.
912
1cdf5ead2a16 Refactor interface method for Schrodinger2d
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diff changeset
202 % Fields:
939
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
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parents: 912
diff changeset
203 % -- interpolation: type of interpolation, default 'none'
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parents: 912
diff changeset
204 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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diff changeset
205
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
206 defaultType.interpolation = 'none';
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
207 default_struct('type', defaultType);
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diff changeset
208
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Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
209 switch type.interpolation
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
210 case {'none', ''}
940
31186559236d Add forgotten type argument in call to interfaceStandard in Schrodinger2d and LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 939
diff changeset
211 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
939
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
212 case {'op','OP'}
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
213 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
214 otherwise
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
215 error('Unknown type of interpolation: %s ', type.interpolation);
912
1cdf5ead2a16 Refactor interface method for Schrodinger2d
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
216 end
1cdf5ead2a16 Refactor interface method for Schrodinger2d
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
217 end
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Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
218
939
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
219 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
718
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parents:
diff changeset
220 % u denotes the solution in the own domain
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
221 % v denotes the solution in the neighbour domain
719
b3f8fb9cefd2 Add interpolation to Schrödinger 2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 718
diff changeset
222
912
1cdf5ead2a16 Refactor interface method for Schrodinger2d
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
223 % Get boundary operators
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Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
224 [e_neighbour, d_neighbour] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
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parents: 910
diff changeset
225 [e, d, H_gamma] = obj.get_boundary_ops(boundary);
719
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parents: 718
diff changeset
226 Hi = obj.Hi;
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diff changeset
227 a = obj.a;
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diff changeset
228
912
1cdf5ead2a16 Refactor interface method for Schrodinger2d
Martin Almquist <malmquist@stanford.edu>
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diff changeset
229 % Get outward unit normal component
1cdf5ead2a16 Refactor interface method for Schrodinger2d
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
230 [~, n] = obj.get_boundary_number(boundary);
719
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diff changeset
231
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Martin Almquist <malmquist@stanford.edu>
parents: 718
diff changeset
232 Hi = obj.Hi;
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Martin Almquist <malmquist@stanford.edu>
parents: 718
diff changeset
233 sigma = -n*1i*a/2;
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Martin Almquist <malmquist@stanford.edu>
parents: 718
diff changeset
234 tau = -n*(1i*a)'/2;
b3f8fb9cefd2 Add interpolation to Schrödinger 2D scheme.
Martin Almquist <malmquist@stanford.edu>
parents: 718
diff changeset
235
912
1cdf5ead2a16 Refactor interface method for Schrodinger2d
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
236 closure = tau*Hi*d*H_gamma*e' + sigma*Hi*e*H_gamma*d';
1cdf5ead2a16 Refactor interface method for Schrodinger2d
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parents: 910
diff changeset
237 penalty = -tau*Hi*d*H_gamma*e_neighbour' ...
1cdf5ead2a16 Refactor interface method for Schrodinger2d
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parents: 910
diff changeset
238 -sigma*Hi*e*H_gamma*d_neighbour';
719
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parents: 718
diff changeset
239
912
1cdf5ead2a16 Refactor interface method for Schrodinger2d
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
240 end
1cdf5ead2a16 Refactor interface method for Schrodinger2d
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
241
939
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
242 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
243
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
244 % User can request special interpolation operators by specifying type.interpOpSet
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
245 default_field(type, 'interpOpSet', @sbp.InterpOpsOP);
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
246 interpOpSet = type.interpOpSet;
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
247
912
1cdf5ead2a16 Refactor interface method for Schrodinger2d
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
248 % u denotes the solution in the own domain
1cdf5ead2a16 Refactor interface method for Schrodinger2d
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
249 % v denotes the solution in the neighbour domain
939
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
250 [e_v, d_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
46f5dc61d90b Update Schrodinger2d to work with new interface types, similar to LaplCurv.
Martin Almquist <malmquist@stanford.edu>
parents: 912
diff changeset
251 [e_u, d_u, H_gamma] = obj.get_boundary_ops(boundary);
912
1cdf5ead2a16 Refactor interface method for Schrodinger2d
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parents: 910
diff changeset
252 Hi = obj.Hi;
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parents: 910
diff changeset
253 a = obj.a;
1cdf5ead2a16 Refactor interface method for Schrodinger2d
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parents: 910
diff changeset
254
1cdf5ead2a16 Refactor interface method for Schrodinger2d
Martin Almquist <malmquist@stanford.edu>
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255 % Get outward unit normal component
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256 [~, n] = obj.get_boundary_number(boundary);
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257
939
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258 % Find the number of grid points along the interface
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259 m_u = size(e_u, 2);
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260 m_v = size(e_v, 2);
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261
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262 % Build interpolation operators
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263 intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order);
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264 Iu2v = intOps.Iu2v;
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265 Iv2u = intOps.Iv2u;
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266
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267 sigma = -n*1i*a/2;
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268 tau = -n*(1i*a)'/2;
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269
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270 closure = tau*Hi*d_u*H_gamma*e_u' + sigma*Hi*e_u*H_gamma*d_u';
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271 penalty = -tau*Hi*d_u*H_gamma*Iv2u.good*e_v' ...
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272 -sigma*Hi*e_u*H_gamma*Iv2u.bad*d_v';
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273
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274 end
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275
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276 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
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277 function [j, nj] = get_boundary_number(obj, boundary)
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278
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279 switch boundary
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280 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
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281 j = 1;
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282 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
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283 j = 2;
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284 otherwise
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285 error('No such boundary: boundary = %s',boundary);
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286 end
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287
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288 switch boundary
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289 case {'w','W','west','West','s','S','south','South'}
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290 nj = -1;
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291 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
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292 nj = 1;
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293 end
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294 end
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295
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296 % Returns the boundary ops and sign for the boundary specified by the string boundary.
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297 % The right boundary is considered the positive boundary
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298 function [e, d, H_b] = get_boundary_ops(obj, boundary)
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299
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300 switch boundary
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301 case 'w'
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302 e = obj.e_w;
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303 d = obj.d_w;
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304 H_b = obj.H_boundary{1};
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305 case 'e'
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306 e = obj.e_e;
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307 d = obj.d_e;
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308 H_b = obj.H_boundary{1};
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309 case 's'
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310 e = obj.e_s;
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311 d = obj.d_s;
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312 H_b = obj.H_boundary{2};
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313 case 'n'
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314 e = obj.e_n;
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315 d = obj.d_n;
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316 H_b = obj.H_boundary{2};
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317 otherwise
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318 error('No such boundary: boundary = %s',boundary);
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319 end
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320 end
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321
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322 function N = size(obj)
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323 N = prod(obj.m);
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324 end
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325 end
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326 end