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annotate DiffOps/test/runtests.jl @ 262:f1e90a92ad74 boundary_conditions

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Add Quadrature and InverseQuadrature for Laplace as TensorMappings. Implement and test the 2D case. Fix implementation of apply_transpose for BoundaryQuadrature and add tests.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Tue, 26 Nov 2019 08:28:26 -0800
parents 5571d2c5bf0f
children ce6a2f3f732a
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1 using Test
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2 using DiffOps
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3 using Grids
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4 using SbpOperators
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5 using RegionIndices
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6 using LazyTensors
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8 @testset "Quadrature" begin
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9 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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10 Lx = 2.3
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11 Ly = 5.2
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12 g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
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13 H = Quadrature(op,g)
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14 v = ones(Float64, size(g))
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15
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16 @test H isa TensorMapping{T,2,2} where T
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17 @test H' isa TensorMapping{T,2,2} where T
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18 @test sum(collect(H*v)) ≈ (Lx*Ly)
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19 @test collect(H*v) == collect(H'*v)
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20 end
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21
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22 @testset "InverseQuadrature" begin
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23 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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24 Lx = 7.3
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25 Ly = 8.2
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26 g = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
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27 H = Quadrature(op,g)
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28 Hinv = InverseQuadrature(op,g)
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29 v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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30
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31 @test Hinv isa TensorMapping{T,2,2} where T
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32 @test Hinv' isa TensorMapping{T,2,2} where T
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33 @test collect(Hinv*H*v) ≈ v
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34 @test collect(Hinv*v) == collect(Hinv'*v)
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35 end
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36
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37 @testset "BoundaryValue" begin
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38 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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39 g = EquidistantGrid((4,5), (0.0, 0.0), (1.0,1.0))
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41 e_w = BoundaryValue(op, g, CartesianBoundary{1,Lower}())
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42 e_e = BoundaryValue(op, g, CartesianBoundary{1,Upper}())
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43 e_s = BoundaryValue(op, g, CartesianBoundary{2,Lower}())
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44 e_n = BoundaryValue(op, g, CartesianBoundary{2,Upper}())
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45
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46 v = zeros(Float64, 4, 5)
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47 v[:,5] = [1, 2, 3,4]
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48 v[:,4] = [1, 2, 3,4]
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49 v[:,3] = [4, 5, 6, 7]
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50 v[:,2] = [7, 8, 9, 10]
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51 v[:,1] = [10, 11, 12, 13]
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52
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53 @test e_w isa TensorMapping{T,2,1} where T
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54 @test e_w' isa TensorMapping{T,1,2} where T
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55
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56 @test domain_size(e_w, (3,2)) == (2,)
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57 @test domain_size(e_e, (3,2)) == (2,)
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58 @test domain_size(e_s, (3,2)) == (3,)
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59 @test domain_size(e_n, (3,2)) == (3,)
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61 @test size(e_w'*v) == (5,)
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62 @test size(e_e'*v) == (5,)
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63 @test size(e_s'*v) == (4,)
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64 @test size(e_n'*v) == (4,)
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65
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66 @test collect(e_w'*v) == [10,7,4,1.0,1]
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67 @test collect(e_e'*v) == [13,10,7,4,4.0]
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68 @test collect(e_s'*v) == [10,11,12,13.0]
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69 @test collect(e_n'*v) == [1,2,3,4.0]
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71 g_x = [1,2,3,4.0]
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72 g_y = [5,4,3,2,1.0]
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73
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74 G_w = zeros(Float64, (4,5))
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75 G_w[1,:] = g_y
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76
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77 G_e = zeros(Float64, (4,5))
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78 G_e[4,:] = g_y
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79
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80 G_s = zeros(Float64, (4,5))
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81 G_s[:,1] = g_x
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82
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83 G_n = zeros(Float64, (4,5))
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84 G_n[:,5] = g_x
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86 @test size(e_w*g_y) == (4,5)
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87 @test size(e_e*g_y) == (4,5)
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88 @test size(e_s*g_x) == (4,5)
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89 @test size(e_n*g_x) == (4,5)
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90
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91 @test collect(e_w*g_y) == G_w
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92 @test collect(e_e*g_y) == G_e
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93 @test collect(e_s*g_x) == G_s
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94 @test collect(e_n*g_x) == G_n
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95 end
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97 @testset "NormalDerivative" begin
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98 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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99 g = EquidistantGrid((5,6), (0.0, 0.0), (4.0,5.0))
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100
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101 d_w = NormalDerivative(op, g, CartesianBoundary{1,Lower}())
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102 d_e = NormalDerivative(op, g, CartesianBoundary{1,Upper}())
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103 d_s = NormalDerivative(op, g, CartesianBoundary{2,Lower}())
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104 d_n = NormalDerivative(op, g, CartesianBoundary{2,Upper}())
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106
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107 v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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108 v∂x = evalOn(g, (x,y)-> 2*x + y)
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109 v∂y = evalOn(g, (x,y)-> 2*(y-1) + x)
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110
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111 @test d_w isa TensorMapping{T,2,1} where T
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112 @test d_w' isa TensorMapping{T,1,2} where T
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114 @test domain_size(d_w, (3,2)) == (2,)
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115 @test domain_size(d_e, (3,2)) == (2,)
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116 @test domain_size(d_s, (3,2)) == (3,)
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117 @test domain_size(d_n, (3,2)) == (3,)
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118
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119 @test size(d_w'*v) == (6,)
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120 @test size(d_e'*v) == (6,)
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121 @test size(d_s'*v) == (5,)
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122 @test size(d_n'*v) == (5,)
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123
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124 @test collect(d_w'*v) ≈ v∂x[1,:]
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125 @test collect(d_e'*v) ≈ v∂x[5,:]
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126 @test collect(d_s'*v) ≈ v∂y[:,1]
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127 @test collect(d_n'*v) ≈ v∂y[:,6]
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128
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129
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130 d_x_l = zeros(Float64, 5)
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131 d_x_u = zeros(Float64, 5)
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132 for i ∈ eachindex(d_x_l)
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133 d_x_l[i] = op.dClosure[i-1]
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134 d_x_u[i] = -op.dClosure[length(d_x_u)-i]
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135 end
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136
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137 d_y_l = zeros(Float64, 6)
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138 d_y_u = zeros(Float64, 6)
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139 for i ∈ eachindex(d_y_l)
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140 d_y_l[i] = op.dClosure[i-1]
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141 d_y_u[i] = -op.dClosure[length(d_y_u)-i]
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142 end
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143
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144 function ❓(x,y)
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145 G = zeros(Float64, length(x), length(y))
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146 for I ∈ CartesianIndices(G)
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147 G[I] = x[I[1]]*y[I[2]]
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148 end
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149
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150 return G
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151 end
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152
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153 g_x = [1,2,3,4.0,5]
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154 g_y = [5,4,3,2,1.0,11]
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155
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156 G_w = ❓(d_x_l, g_y)
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157 G_e = ❓(d_x_u, g_y)
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158 G_s = ❓(g_x, d_y_l)
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159 G_n = ❓(g_x, d_y_u)
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160
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161
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162 @test size(d_w*g_y) == (5,6)
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163 @test size(d_e*g_y) == (5,6)
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164 @test size(d_s*g_x) == (5,6)
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165 @test size(d_n*g_x) == (5,6)
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166
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167 @test collect(d_w*g_y) ≈ G_w
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168 @test collect(d_e*g_y) ≈ G_e
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169 @test collect(d_s*g_x) ≈ G_s
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170 @test collect(d_n*g_x) ≈ G_n
235
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171 end
259
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172
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173 @testset "BoundaryQuadrature" begin
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174 op = readOperator(sbp_operators_path()*"d2_4th.txt",sbp_operators_path()*"h_4th.txt")
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175 g = EquidistantGrid((10,11), (0.0, 0.0), (1.0,1.0))
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176
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177 H_w = BoundaryQuadrature(op, g, CartesianBoundary{1,Lower}())
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178 H_e = BoundaryQuadrature(op, g, CartesianBoundary{1,Upper}())
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179 H_s = BoundaryQuadrature(op, g, CartesianBoundary{2,Lower}())
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180 H_n = BoundaryQuadrature(op, g, CartesianBoundary{2,Upper}())
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181
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182 v = evalOn(g, (x,y)-> x^2 + (y-1)^2 + x*y)
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183
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184 function get_quadrature(N)
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185 qc = op.quadratureClosure
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186 q = (qc..., ones(N-2*closuresize(op))..., reverse(qc)...)
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187 @assert length(q) == N
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188 return q
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189 end
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190
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191 v_w = v[1,:]
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192 v_e = v[10,:]
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193 v_s = v[:,1]
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194 v_n = v[:,11]
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195
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196 q_x = spacing(g)[1].*get_quadrature(10)
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197 q_y = spacing(g)[2].*get_quadrature(11)
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198
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199 @test H_w isa TensorOperator{T,1} where T
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200
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201 @test domain_size(H_w, (3,)) == (3,)
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202 @test domain_size(H_n, (3,)) == (3,)
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203
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204 @test range_size(H_w, (3,)) == (3,)
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205 @test range_size(H_n, (3,)) == (3,)
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206
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207 @test size(H_w*v_w) == (11,)
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208 @test size(H_e*v_e) == (11,)
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209 @test size(H_s*v_s) == (10,)
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210 @test size(H_n*v_n) == (10,)
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211
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212 @test collect(H_w*v_w) ≈ q_y.*v_w
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213 @test collect(H_e*v_e) ≈ q_y.*v_e
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214 @test collect(H_s*v_s) ≈ q_x.*v_s
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215 @test collect(H_n*v_n) ≈ q_x.*v_n
262
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216
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217 @test collect(H_w'*v_w) == collect(H_w'*v_w)
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218 @test collect(H_e'*v_e) == collect(H_e'*v_e)
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219 @test collect(H_s'*v_s) == collect(H_s'*v_s)
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220 @test collect(H_n'*v_n) == collect(H_n'*v_n)
259
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221 end