Mercurial > repos > public > sbplib_julia
annotate test/SbpOperators/volumeops/laplace/laplace_test.jl @ 869:4bd35ba8f34a feature/laplace_opset
REVIEW: Add a few comments and suggest code changes
| author | Jonatan Werpers <jonatan@werpers.com> |
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| date | Tue, 25 Jan 2022 07:21:58 +0100 |
| parents | 1784b1c0af3e |
| children | 6a4d36eccf39 |
| rev | line source |
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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 |
| 866 | 9 operator_path = sbp_operators_path()*"standard_diagonal.toml" |
| 10 # Default stencils (4th order) | |
| 11 stencil_set = read_stencil_set(operator_path; order=4) | |
| 12 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"]) | |
| 13 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"]) | |
| 14 e_closure = parse_stencil(stencil_set["e"]["closure"]) | |
| 15 d_closure = parse_stencil(stencil_set["d1"]["closure"]) | |
| 16 quadrature_interior = parse_scalar(stencil_set["H"]["inner"]) | |
| 17 quadrature_closure = parse_tuple(stencil_set["H"]["closure"]) | |
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18 |
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19 @testset "Laplace" begin |
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20 g_1D = EquidistantGrid(101, 0.0, 1.) |
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21 g_3D = EquidistantGrid((51,101,52), (0.0, -1.0, 0.0), (1., 1., 1.)) |
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22 @testset "Constructors" begin |
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23 |
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24 @testset "1D" begin |
| 866 | 25 Δ = laplace(g_1D, inner_stencil, closure_stencils) |
| 26 H = inner_product(g_1D, quadrature_interior, quadrature_closure) | |
| 27 Hi = inverse_inner_product(g_1D, quadrature_interior, quadrature_closure) | |
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28 |
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29 (id_l, id_r) = boundary_identifiers(g_1D) |
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30 |
| 866 | 31 e_l = boundary_restriction(g_1D, e_closure,id_l) |
| 32 e_r = boundary_restriction(g_1D, e_closure,id_r) | |
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33 e_dict = StaticDict(id_l => e_l, id_r => e_r) |
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34 |
| 866 | 35 d_l = normal_derivative(g_1D, d_closure,id_l) |
| 36 d_r = normal_derivative(g_1D, d_closure,id_r) | |
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37 d_dict = StaticDict(id_l => d_l, id_r => d_r) |
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38 |
| 866 | 39 H_l = inner_product(boundary_grid(g_1D,id_l), quadrature_interior, quadrature_closure) |
| 40 H_r = inner_product(boundary_grid(g_1D,id_r), quadrature_interior, quadrature_closure) | |
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41 Hb_dict = StaticDict(id_l => H_l, id_r => H_r) |
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42 |
| 866 | 43 L = Laplace(g_1D, operator_path; order=4) |
| 44 @test L == Laplace(Δ, H, Hi, e_dict, d_dict, Hb_dict) | |
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45 @test L isa TensorMapping{T,1,1} where T |
| 866 | 46 @inferred Laplace(Δ, H, Hi, e_dict, d_dict, Hb_dict) |
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47 end |
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48 @testset "3D" begin |
| 866 | 49 Δ = laplace(g_3D, inner_stencil, closure_stencils) |
| 50 H = inner_product(g_3D, quadrature_interior, quadrature_closure) | |
| 51 Hi = inverse_inner_product(g_3D, quadrature_interior, quadrature_closure) | |
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52 |
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53 (id_l, id_r, id_s, id_n, id_b, id_t) = boundary_identifiers(g_3D) |
| 866 | 54 e_l = boundary_restriction(g_3D, e_closure,id_l) |
| 55 e_r = boundary_restriction(g_3D, e_closure,id_r) | |
| 56 e_s = boundary_restriction(g_3D, e_closure,id_s) | |
| 57 e_n = boundary_restriction(g_3D, e_closure,id_n) | |
| 58 e_b = boundary_restriction(g_3D, e_closure,id_b) | |
| 59 e_t = boundary_restriction(g_3D, e_closure,id_t) | |
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60 e_dict = StaticDict(id_l => e_l, id_r => e_r, |
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61 id_s => e_s, id_n => e_n, |
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62 id_b => e_b, id_t => e_t) |
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63 |
| 866 | 64 d_l = normal_derivative(g_3D, d_closure,id_l) |
| 65 d_r = normal_derivative(g_3D, d_closure,id_r) | |
| 66 d_s = normal_derivative(g_3D, d_closure,id_s) | |
| 67 d_n = normal_derivative(g_3D, d_closure,id_n) | |
| 68 d_b = normal_derivative(g_3D, d_closure,id_b) | |
| 69 d_t = normal_derivative(g_3D, d_closure,id_t) | |
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70 d_dict = StaticDict(id_l => d_l, id_r => d_r, |
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71 id_s => d_s, id_n => d_n, |
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72 id_b => d_b, id_t => d_t) |
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73 |
| 866 | 74 H_l = inner_product(boundary_grid(g_3D,id_l), quadrature_interior, quadrature_closure) |
| 75 H_r = inner_product(boundary_grid(g_3D,id_r), quadrature_interior, quadrature_closure) | |
| 76 H_s = inner_product(boundary_grid(g_3D,id_s), quadrature_interior, quadrature_closure) | |
| 77 H_n = inner_product(boundary_grid(g_3D,id_n), quadrature_interior, quadrature_closure) | |
| 78 H_b = inner_product(boundary_grid(g_3D,id_b), quadrature_interior, quadrature_closure) | |
| 79 H_t = inner_product(boundary_grid(g_3D,id_t), quadrature_interior, quadrature_closure) | |
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80 Hb_dict = StaticDict(id_l => H_l, id_r => H_r, |
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81 id_s => H_s, id_n => H_n, |
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82 id_b => H_b, id_t => H_t) |
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83 |
| 866 | 84 L = Laplace(g_3D, operator_path; order=4) |
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85 @test L == Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict) |
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86 @test L isa TensorMapping{T,3,3} where T |
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87 @inferred Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict) |
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88 end |
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89 end |
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90 |
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91 @testset "laplace" begin |
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92 @testset "1D" begin |
| 799 | 93 L = laplace(g_1D, inner_stencil, closure_stencils) |
| 94 @test L == second_derivative(g_1D, inner_stencil, closure_stencils) | |
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95 @test L isa TensorMapping{T,1,1} where T |
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96 end |
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97 @testset "3D" begin |
| 799 | 98 L = laplace(g_3D, inner_stencil, closure_stencils) |
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99 @test L isa TensorMapping{T,3,3} where T |
| 799 | 100 Dxx = second_derivative(g_3D, inner_stencil, closure_stencils, 1) |
| 101 Dyy = second_derivative(g_3D, inner_stencil, closure_stencils, 2) | |
| 102 Dzz = second_derivative(g_3D, inner_stencil, closure_stencils, 3) | |
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103 @test L == Dxx + Dyy + Dzz |
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104 @test L isa TensorMapping{T,3,3} where T |
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105 end |
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106 end |
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107 |
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108 @testset "inner_product" begin |
| 866 | 109 L = Laplace(g_3D, operator_path; order=4) |
| 110 @test inner_product(L) == inner_product(g_3D, quadrature_interior, quadrature_closure) | |
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111 end |
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112 |
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113 @testset "inverse_inner_product" begin |
| 866 | 114 L = Laplace(g_3D, operator_path; order=4) |
| 115 @test inverse_inner_product(L) == inverse_inner_product(g_3D, quadrature_interior, quadrature_closure) | |
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116 end |
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117 |
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118 @testset "boundary_restriction" begin |
| 866 | 119 L = Laplace(g_3D, operator_path; order=4) |
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120 (id_l, id_r, id_s, id_n, id_b, id_t) = boundary_identifiers(g_3D) |
| 866 | 121 @test boundary_restriction(L, id_l) == boundary_restriction(g_3D, e_closure,id_l) |
| 122 @test boundary_restriction(L, id_r) == boundary_restriction(g_3D, e_closure,id_r) | |
| 123 @test boundary_restriction(L, id_s) == boundary_restriction(g_3D, e_closure,id_s) | |
| 124 @test boundary_restriction(L, id_n) == boundary_restriction(g_3D, e_closure,id_n) | |
| 125 @test boundary_restriction(L, id_b) == boundary_restriction(g_3D, e_closure,id_b) | |
| 126 @test boundary_restriction(L, id_t) == boundary_restriction(g_3D, e_closure,id_t) | |
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127 |
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128 ids = boundary_identifiers(g_3D) |
| 866 | 129 es = boundary_restriction(L, ids) |
| 130 @test es == (boundary_restriction(L, id_l), | |
| 131 boundary_restriction(L, id_r), | |
| 132 boundary_restriction(L, id_s), | |
| 133 boundary_restriction(L, id_n), | |
| 134 boundary_restriction(L, id_b), | |
| 135 boundary_restriction(L, id_t)); | |
| 136 @test es == boundary_restriction(L, ids...) | |
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137 end |
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138 |
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139 @testset "normal_derivative" begin |
| 866 | 140 L = Laplace(g_3D, operator_path; order=4) |
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141 (id_l, id_r, id_s, id_n, id_b, id_t) = boundary_identifiers(g_3D) |
| 866 | 142 @test normal_derivative(L, id_l) == normal_derivative(g_3D, d_closure,id_l) |
| 143 @test normal_derivative(L, id_r) == normal_derivative(g_3D, d_closure,id_r) | |
| 144 @test normal_derivative(L, id_s) == normal_derivative(g_3D, d_closure,id_s) | |
| 145 @test normal_derivative(L, id_n) == normal_derivative(g_3D, d_closure,id_n) | |
| 146 @test normal_derivative(L, id_b) == normal_derivative(g_3D, d_closure,id_b) | |
| 147 @test normal_derivative(L, id_t) == normal_derivative(g_3D, d_closure,id_t) | |
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148 |
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149 ids = boundary_identifiers(g_3D) |
| 866 | 150 ds = normal_derivative(L, ids) |
| 151 @test ds == (normal_derivative(L, id_l), | |
| 152 normal_derivative(L, id_r), | |
| 153 normal_derivative(L, id_s), | |
| 154 normal_derivative(L, id_n), | |
| 155 normal_derivative(L, id_b), | |
| 156 normal_derivative(L, id_t)); | |
| 157 @test ds == normal_derivative(L, ids...) | |
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158 end |
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159 |
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160 @testset "boundary_quadrature" begin |
| 866 | 161 L = Laplace(g_3D, operator_path; order=4) |
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162 (id_l, id_r, id_s, id_n, id_b, id_t) = boundary_identifiers(g_3D) |
| 866 | 163 @test boundary_quadrature(L, id_l) == inner_product(boundary_grid(g_3D, id_l), quadrature_interior, quadrature_closure) |
| 164 @test boundary_quadrature(L, id_r) == inner_product(boundary_grid(g_3D, id_r), quadrature_interior, quadrature_closure) | |
| 165 @test boundary_quadrature(L, id_s) == inner_product(boundary_grid(g_3D, id_s), quadrature_interior, quadrature_closure) | |
| 166 @test boundary_quadrature(L, id_n) == inner_product(boundary_grid(g_3D, id_n), quadrature_interior, quadrature_closure) | |
| 167 @test boundary_quadrature(L, id_b) == inner_product(boundary_grid(g_3D, id_b), quadrature_interior, quadrature_closure) | |
| 168 @test boundary_quadrature(L, id_t) == inner_product(boundary_grid(g_3D, id_t), quadrature_interior, quadrature_closure) | |
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169 |
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170 ids = boundary_identifiers(g_3D) |
| 866 | 171 H_gammas = boundary_quadrature(L, ids) |
| 172 @test H_gammas == (boundary_quadrature(L, id_l), | |
| 173 boundary_quadrature(L, id_r), | |
| 174 boundary_quadrature(L, id_s), | |
| 175 boundary_quadrature(L, id_n), | |
| 176 boundary_quadrature(L, id_b), | |
| 177 boundary_quadrature(L, id_t)); | |
| 178 @test H_gammas == boundary_quadrature(L, ids...) | |
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179 end |
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180 |
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181 # Exact differentiation is measured point-wise. In other cases |
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182 # the error is measured in the l2-norm. |
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183 @testset "Accuracy" begin |
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184 l2(v) = sqrt(prod(spacing(g_3D))*sum(v.^2)); |
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185 polynomials = () |
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186 maxOrder = 4; |
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187 for i = 0:maxOrder-1 |
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188 f_i(x,y,z) = 1/factorial(i)*(y^i + x^i + z^i) |
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189 polynomials = (polynomials...,evalOn(g_3D,f_i)) |
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190 end |
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191 v = evalOn(g_3D, (x,y,z) -> sin(x) + cos(y) + exp(z)) |
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192 Δv = evalOn(g_3D,(x,y,z) -> -sin(x) - cos(y) + exp(z)) |
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193 |
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194 # 2nd order interior stencil, 1st order boundary stencil, |
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195 # implies that L*v should be exact for binomials up to order 2. |
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196 @testset "2nd order" begin |
| 866 | 197 stencil_set = read_stencil_set(operator_path; order=2) |
| 799 | 198 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"]) |
| 199 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"]) | |
| 200 L = laplace(g_3D, inner_stencil, closure_stencils) | |
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201 @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9 |
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202 @test L*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9 |
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203 @test L*polynomials[3] ≈ polynomials[1] atol = 5e-9 |
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204 @test L*v ≈ Δv rtol = 5e-2 norm = l2 |
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205 end |
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206 |
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207 # 4th order interior stencil, 2nd order boundary stencil, |
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208 # implies that L*v should be exact for binomials up to order 3. |
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209 @testset "4th order" begin |
| 866 | 210 stencil_set = read_stencil_set(operator_path; order=4) |
| 799 | 211 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"]) |
| 212 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"]) | |
| 213 L = laplace(g_3D, inner_stencil, closure_stencils) | |
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214 # NOTE: high tolerances for checking the "exact" differentiation |
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215 # due to accumulation of round-off errors/cancellation errors? |
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216 @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9 |
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217 @test L*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9 |
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218 @test L*polynomials[3] ≈ polynomials[1] atol = 5e-9 |
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219 @test L*polynomials[4] ≈ polynomials[2] atol = 5e-9 |
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220 @test L*v ≈ Δv rtol = 5e-4 norm = l2 |
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221 end |
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222 end |
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223 end |