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annotate test/SbpOperators/volumeops/laplace/laplace_test.jl @ 754:dc38e57ebd1b feature/laplace_opset

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Add convenience functions for returning multiple boundary operators from Laplace
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Sun, 21 Mar 2021 13:44:29 +0100
parents fc83d672be36
children 1784b1c0af3e
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45966c77cb20 Split tests for SbpOperators over several files
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1 using Test
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2
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3 using Sbplib.SbpOperators
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4 using Sbplib.Grids
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5 using Sbplib.LazyTensors
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6 using Sbplib.RegionIndices
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7 using Sbplib.StaticDicts
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8
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9 @testset "Laplace" begin
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10 g_1D = EquidistantGrid(101, 0.0, 1.)
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11 g_3D = EquidistantGrid((51,101,52), (0.0, -1.0, 0.0), (1., 1., 1.))
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12 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
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13 @testset "Constructors" begin
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14
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15 @testset "1D" begin
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16 # Create all tensor mappings included in Laplace
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17 Δ = laplace(g_1D, op.innerStencil, op.closureStencils)
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18 H = inner_product(g_1D, op.quadratureClosure)
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19 Hi = inverse_inner_product(g_1D, op.quadratureClosure)
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20
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21 (id_l, id_r) = boundary_identifiers(g_1D)
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22
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23 e_l = boundary_restriction(g_1D,op.eClosure,id_l)
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24 e_r = boundary_restriction(g_1D,op.eClosure,id_r)
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25 e_dict = StaticDict(id_l => e_l, id_r => e_r)
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26
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27 d_l = normal_derivative(g_1D,op.dClosure,id_l)
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28 d_r = normal_derivative(g_1D,op.dClosure,id_r)
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29 d_dict = StaticDict(id_l => d_l, id_r => d_r)
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30
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31 H_l = inner_product(boundary_grid(g_1D,id_l),op.quadratureClosure)
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32 H_r = inner_product(boundary_grid(g_1D,id_r),op.quadratureClosure)
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33 Hb_dict = StaticDict(id_l => H_l, id_r => H_r)
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34
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35 L = Laplace(g_1D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
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36 @test L == Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict)
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37 @test L isa TensorMapping{T,1,1} where T
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38 @inferred Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict)
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39 end
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40 @testset "3D" begin
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41 # Create all tensor mappings included in Laplace
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42 Δ = laplace(g_3D, op.innerStencil, op.closureStencils)
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43 H = inner_product(g_3D, op.quadratureClosure)
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44 Hi = inverse_inner_product(g_3D, op.quadratureClosure)
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45
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46 (id_l, id_r, id_s, id_n, id_b, id_t) = boundary_identifiers(g_3D)
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47 e_l = boundary_restriction(g_3D,op.eClosure,id_l)
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48 e_r = boundary_restriction(g_3D,op.eClosure,id_r)
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49 e_s = boundary_restriction(g_3D,op.eClosure,id_s)
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50 e_n = boundary_restriction(g_3D,op.eClosure,id_n)
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51 e_b = boundary_restriction(g_3D,op.eClosure,id_b)
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52 e_t = boundary_restriction(g_3D,op.eClosure,id_t)
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53 e_dict = StaticDict(id_l => e_l, id_r => e_r,
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54 id_s => e_s, id_n => e_n,
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55 id_b => e_b, id_t => e_t)
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56
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57 d_l = normal_derivative(g_3D,op.dClosure,id_l)
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58 d_r = normal_derivative(g_3D,op.dClosure,id_r)
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59 d_s = normal_derivative(g_3D,op.dClosure,id_s)
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60 d_n = normal_derivative(g_3D,op.dClosure,id_n)
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61 d_b = normal_derivative(g_3D,op.dClosure,id_b)
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62 d_t = normal_derivative(g_3D,op.dClosure,id_t)
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63 d_dict = StaticDict(id_l => d_l, id_r => d_r,
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64 id_s => d_s, id_n => d_n,
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65 id_b => d_b, id_t => d_t)
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66
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67 H_l = inner_product(boundary_grid(g_3D,id_l),op.quadratureClosure)
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68 H_r = inner_product(boundary_grid(g_3D,id_r),op.quadratureClosure)
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69 H_s = inner_product(boundary_grid(g_3D,id_s),op.quadratureClosure)
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70 H_n = inner_product(boundary_grid(g_3D,id_n),op.quadratureClosure)
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71 H_b = inner_product(boundary_grid(g_3D,id_b),op.quadratureClosure)
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72 H_t = inner_product(boundary_grid(g_3D,id_t),op.quadratureClosure)
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73 Hb_dict = StaticDict(id_l => H_l, id_r => H_r,
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74 id_s => H_s, id_n => H_n,
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75 id_b => H_b, id_t => H_t)
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76
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77 L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
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78 @test L == Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict)
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79 @test L isa TensorMapping{T,3,3} where T
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80 @inferred Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict)
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81 end
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82 end
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83
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84 @testset "laplace" begin
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85 @testset "1D" begin
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86 L = laplace(g_1D, op.innerStencil, op.closureStencils)
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87 @test L == second_derivative(g_1D, op.innerStencil, op.closureStencils)
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88 @test L isa TensorMapping{T,1,1} where T
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89 end
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90 @testset "3D" begin
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91 L = laplace(g_3D, op.innerStencil, op.closureStencils)
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92 @test L isa TensorMapping{T,3,3} where T
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93 Dxx = second_derivative(g_3D, op.innerStencil, op.closureStencils,1)
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94 Dyy = second_derivative(g_3D, op.innerStencil, op.closureStencils,2)
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95 Dzz = second_derivative(g_3D, op.innerStencil, op.closureStencils,3)
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96 @test L == Dxx + Dyy + Dzz
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97 @test L isa TensorMapping{T,3,3} where T
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98 end
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99 end
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100
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101 @testset "inner_product" begin
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102 L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
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103 @test inner_product(L) == inner_product(g_3D,op.quadratureClosure)
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104 end
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105
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106 @testset "inverse_inner_product" begin
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107 L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
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108 @test inverse_inner_product(L) == inverse_inner_product(g_3D,op.quadratureClosure)
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109 end
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110
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111 @testset "boundary_restriction" begin
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112 L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
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113 (id_l, id_r, id_s, id_n, id_b, id_t) = boundary_identifiers(g_3D)
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114 @test boundary_restriction(L,id_l) == boundary_restriction(g_3D,op.eClosure,id_l)
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115 @test boundary_restriction(L,id_r) == boundary_restriction(g_3D,op.eClosure,id_r)
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116 @test boundary_restriction(L,id_s) == boundary_restriction(g_3D,op.eClosure,id_s)
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117 @test boundary_restriction(L,id_n) == boundary_restriction(g_3D,op.eClosure,id_n)
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118 @test boundary_restriction(L,id_b) == boundary_restriction(g_3D,op.eClosure,id_b)
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119 @test boundary_restriction(L,id_t) == boundary_restriction(g_3D,op.eClosure,id_t)
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120
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121 ids = boundary_identifiers(g_3D)
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122 es = boundary_restriction(L,ids)
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123 @test es == (boundary_restriction(L,id_l),
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124 boundary_restriction(L,id_r),
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125 boundary_restriction(L,id_s),
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126 boundary_restriction(L,id_n),
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127 boundary_restriction(L,id_b),
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128 boundary_restriction(L,id_t));
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129 @test es == boundary_restriction(L,ids...)
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130 end
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131
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132 @testset "normal_derivative" begin
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133 L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
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134 (id_l, id_r, id_s, id_n, id_b, id_t) = boundary_identifiers(g_3D)
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135 @test normal_derivative(L,id_l) == normal_derivative(g_3D,op.dClosure,id_l)
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136 @test normal_derivative(L,id_r) == normal_derivative(g_3D,op.dClosure,id_r)
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137 @test normal_derivative(L,id_s) == normal_derivative(g_3D,op.dClosure,id_s)
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138 @test normal_derivative(L,id_n) == normal_derivative(g_3D,op.dClosure,id_n)
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139 @test normal_derivative(L,id_b) == normal_derivative(g_3D,op.dClosure,id_b)
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140 @test normal_derivative(L,id_t) == normal_derivative(g_3D,op.dClosure,id_t)
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141
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142 ids = boundary_identifiers(g_3D)
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143 ds = normal_derivative(L,ids)
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144 @test ds == (normal_derivative(L,id_l),
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145 normal_derivative(L,id_r),
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146 normal_derivative(L,id_s),
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147 normal_derivative(L,id_n),
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148 normal_derivative(L,id_b),
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149 normal_derivative(L,id_t));
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150 @test ds == normal_derivative(L,ids...)
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151 end
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152
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153 @testset "boundary_quadrature" begin
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154 L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
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155 (id_l, id_r, id_s, id_n, id_b, id_t) = boundary_identifiers(g_3D)
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156 @test boundary_quadrature(L,id_l) == inner_product(boundary_grid(g_3D,id_l),op.quadratureClosure)
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157 @test boundary_quadrature(L,id_r) == inner_product(boundary_grid(g_3D,id_r),op.quadratureClosure)
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158 @test boundary_quadrature(L,id_s) == inner_product(boundary_grid(g_3D,id_s),op.quadratureClosure)
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159 @test boundary_quadrature(L,id_n) == inner_product(boundary_grid(g_3D,id_n),op.quadratureClosure)
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160 @test boundary_quadrature(L,id_b) == inner_product(boundary_grid(g_3D,id_b),op.quadratureClosure)
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161 @test boundary_quadrature(L,id_t) == inner_product(boundary_grid(g_3D,id_t),op.quadratureClosure)
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162
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163 ids = boundary_identifiers(g_3D)
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164 H_gammas = boundary_quadrature(L,ids)
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165 @test H_gammas == (boundary_quadrature(L,id_l),
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166 boundary_quadrature(L,id_r),
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167 boundary_quadrature(L,id_s),
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168 boundary_quadrature(L,id_n),
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169 boundary_quadrature(L,id_b),
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170 boundary_quadrature(L,id_t));
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171 @test H_gammas == boundary_quadrature(L,ids...)
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172 end
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173
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174 # Exact differentiation is measured point-wise. In other cases
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175 # the error is measured in the l2-norm.
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176 @testset "Accuracy" begin
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177 l2(v) = sqrt(prod(spacing(g_3D))*sum(v.^2));
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178 polynomials = ()
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179 maxOrder = 4;
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180 for i = 0:maxOrder-1
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181 f_i(x,y,z) = 1/factorial(i)*(y^i + x^i + z^i)
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182 polynomials = (polynomials...,evalOn(g_3D,f_i))
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183 end
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184 v = evalOn(g_3D, (x,y,z) -> sin(x) + cos(y) + exp(z))
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185 Δv = evalOn(g_3D,(x,y,z) -> -sin(x) - cos(y) + exp(z))
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186
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187 # 2nd order interior stencil, 1st order boundary stencil,
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188 # implies that L*v should be exact for binomials up to order 2.
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189 @testset "2nd order" begin
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190 L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=2)
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191 @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
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192 @test L*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
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193 @test L*polynomials[3] ≈ polynomials[1] atol = 5e-9
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194 @test L*v ≈ Δv rtol = 5e-2 norm = l2
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195 end
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196
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197 # 4th order interior stencil, 2nd order boundary stencil,
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198 # implies that L*v should be exact for binomials up to order 3.
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199 @testset "4th order" begin
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200 L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
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201 # NOTE: high tolerances for checking the "exact" differentiation
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202 # due to accumulation of round-off errors/cancellation errors?
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203 @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
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204 @test L*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
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205 @test L*polynomials[3] ≈ polynomials[1] atol = 5e-9
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206 @test L*polynomials[4] ≈ polynomials[2] atol = 5e-9
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207 @test L*v ≈ Δv rtol = 5e-4 norm = l2
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208 end
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209 end
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210 end