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comparison test/SbpOperators/SbpOperators_test.jl @ 711:df88aee35bb9 feature/selectable_tests

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Switch to _test.jl suffix
author Jonatan Werpers <jonatan@werpers.com>
date Sat, 20 Feb 2021 20:45:40 +0100
parents test/SbpOperators/testSbpOperators.jl@48a61e085e60
children 11a444d6fc93
comparison
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710:44fa9a171557 711:df88aee35bb9
1 using Test
2 using Sbplib.SbpOperators
3 using Sbplib.Grids
4 using Sbplib.RegionIndices
5 using Sbplib.LazyTensors
6 using LinearAlgebra
7 using TOML
8
9 import Sbplib.SbpOperators.Stencil
10 import Sbplib.SbpOperators.VolumeOperator
11 import Sbplib.SbpOperators.volume_operator
12 import Sbplib.SbpOperators.BoundaryOperator
13 import Sbplib.SbpOperators.boundary_operator
14 import Sbplib.SbpOperators.even
15 import Sbplib.SbpOperators.odd
16
17
18 @testset "SbpOperators" begin
19
20 @testset "Stencil" begin
21 s = Stencil((-2,2), (1.,2.,2.,3.,4.))
22 @test s isa Stencil{Float64, 5}
23
24 @test eltype(s) == Float64
25 @test SbpOperators.scale(s, 2) == Stencil((-2,2), (2.,4.,4.,6.,8.))
26
27 @test Stencil(1,2,3,4; center=1) == Stencil((0, 3),(1,2,3,4))
28 @test Stencil(1,2,3,4; center=2) == Stencil((-1, 2),(1,2,3,4))
29 @test Stencil(1,2,3,4; center=4) == Stencil((-3, 0),(1,2,3,4))
30
31 @test CenteredStencil(1,2,3,4,5) == Stencil((-2, 2), (1,2,3,4,5))
32 @test_throws ArgumentError CenteredStencil(1,2,3,4)
33 end
34
35 @testset "parse_rational" begin
36 @test SbpOperators.parse_rational("1") isa Rational
37 @test SbpOperators.parse_rational("1") == 1//1
38 @test SbpOperators.parse_rational("1/2") isa Rational
39 @test SbpOperators.parse_rational("1/2") == 1//2
40 @test SbpOperators.parse_rational("37/13") isa Rational
41 @test SbpOperators.parse_rational("37/13") == 37//13
42 end
43
44 @testset "readoperator" begin
45 toml_str = """
46 [meta]
47 type = "equidistant"
48
49 [order2]
50 H.inner = ["1"]
51
52 D1.inner_stencil = ["-1/2", "0", "1/2"]
53 D1.closure_stencils = [
54 ["-1", "1"],
55 ]
56
57 d1.closure = ["-3/2", "2", "-1/2"]
58
59 [order4]
60 H.closure = ["17/48", "59/48", "43/48", "49/48"]
61
62 D2.inner_stencil = ["-1/12","4/3","-5/2","4/3","-1/12"]
63 D2.closure_stencils = [
64 [ "2", "-5", "4", "-1", "0", "0"],
65 [ "1", "-2", "1", "0", "0", "0"],
66 [ "-4/43", "59/43", "-110/43", "59/43", "-4/43", "0"],
67 [ "-1/49", "0", "59/49", "-118/49", "64/49", "-4/49"],
68 ]
69 """
70
71 parsed_toml = TOML.parse(toml_str)
72 @testset "get_stencil" begin
73 @test get_stencil(parsed_toml, "order2", "D1", "inner_stencil") == Stencil(-1/2, 0., 1/2, center=2)
74 @test get_stencil(parsed_toml, "order2", "D1", "inner_stencil", center=1) == Stencil(-1/2, 0., 1/2; center=1)
75 @test get_stencil(parsed_toml, "order2", "D1", "inner_stencil", center=3) == Stencil(-1/2, 0., 1/2; center=3)
76
77 @test get_stencil(parsed_toml, "order2", "H", "inner") == Stencil(1.; center=1)
78
79 @test_throws AssertionError get_stencil(parsed_toml, "meta", "type")
80 @test_throws AssertionError get_stencil(parsed_toml, "order2", "D1", "closure_stencils")
81 end
82
83 @testset "get_stencils" begin
84 @test get_stencils(parsed_toml, "order2", "D1", "closure_stencils", centers=(1,)) == (Stencil(-1., 1., center=1),)
85 @test get_stencils(parsed_toml, "order2", "D1", "closure_stencils", centers=(2,)) == (Stencil(-1., 1., center=2),)
86 @test get_stencils(parsed_toml, "order2", "D1", "closure_stencils", centers=[2]) == (Stencil(-1., 1., center=2),)
87
88 @test get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=[1,1,1,1]) == (
89 Stencil( 2., -5., 4., -1., 0., 0., center=1),
90 Stencil( 1., -2., 1., 0., 0., 0., center=1),
91 Stencil( -4/43, 59/43, -110/43, 59/43, -4/43, 0., center=1),
92 Stencil( -1/49, 0., 59/49, -118/49, 64/49, -4/49, center=1),
93 )
94
95 @test get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=(4,2,3,1)) == (
96 Stencil( 2., -5., 4., -1., 0., 0., center=4),
97 Stencil( 1., -2., 1., 0., 0., 0., center=2),
98 Stencil( -4/43, 59/43, -110/43, 59/43, -4/43, 0., center=3),
99 Stencil( -1/49, 0., 59/49, -118/49, 64/49, -4/49, center=1),
100 )
101
102 @test get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=1:4) == (
103 Stencil( 2., -5., 4., -1., 0., 0., center=1),
104 Stencil( 1., -2., 1., 0., 0., 0., center=2),
105 Stencil( -4/43, 59/43, -110/43, 59/43, -4/43, 0., center=3),
106 Stencil( -1/49, 0., 59/49, -118/49, 64/49, -4/49, center=4),
107 )
108
109 @test_throws AssertionError get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=(1,2,3))
110 @test_throws AssertionError get_stencils(parsed_toml, "order4", "D2", "closure_stencils",centers=(1,2,3,5,4))
111 @test_throws AssertionError get_stencils(parsed_toml, "order4", "D2", "inner_stencil",centers=(1,2))
112 end
113
114 @testset "get_tuple" begin
115 @test get_tuple(parsed_toml, "order2", "d1", "closure") == (-3/2, 2, -1/2)
116
117 @test_throws AssertionError get_tuple(parsed_toml, "meta", "type")
118 end
119 end
120
121 @testset "VolumeOperator" begin
122 inner_stencil = CenteredStencil(1/4, 2/4, 1/4)
123 closure_stencils = (Stencil(1/2, 1/2; center=1), Stencil(0.,1.; center=2))
124 g_1D = EquidistantGrid(11,0.,1.)
125 g_2D = EquidistantGrid((11,12),(0.,0.),(1.,1.))
126 g_3D = EquidistantGrid((11,12,10),(0.,0.,0.),(1.,1.,1.))
127 @testset "Constructors" begin
128 @testset "1D" begin
129 op = VolumeOperator(inner_stencil,closure_stencils,(11,),even)
130 @test op == VolumeOperator(g_1D,inner_stencil,closure_stencils,even)
131 @test op == volume_operator(g_1D,inner_stencil,closure_stencils,even,1)
132 @test op isa TensorMapping{T,1,1} where T
133 end
134 @testset "2D" begin
135 op_x = volume_operator(g_2D,inner_stencil,closure_stencils,even,1)
136 op_y = volume_operator(g_2D,inner_stencil,closure_stencils,even,2)
137 Ix = IdentityMapping{Float64}((11,))
138 Iy = IdentityMapping{Float64}((12,))
139 @test op_x == VolumeOperator(inner_stencil,closure_stencils,(11,),even)⊗Iy
140 @test op_y == Ix⊗VolumeOperator(inner_stencil,closure_stencils,(12,),even)
141 @test op_x isa TensorMapping{T,2,2} where T
142 @test op_y isa TensorMapping{T,2,2} where T
143 end
144 @testset "3D" begin
145 op_x = volume_operator(g_3D,inner_stencil,closure_stencils,even,1)
146 op_y = volume_operator(g_3D,inner_stencil,closure_stencils,even,2)
147 op_z = volume_operator(g_3D,inner_stencil,closure_stencils,even,3)
148 Ix = IdentityMapping{Float64}((11,))
149 Iy = IdentityMapping{Float64}((12,))
150 Iz = IdentityMapping{Float64}((10,))
151 @test op_x == VolumeOperator(inner_stencil,closure_stencils,(11,),even)⊗Iy⊗Iz
152 @test op_y == Ix⊗VolumeOperator(inner_stencil,closure_stencils,(12,),even)⊗Iz
153 @test op_z == Ix⊗Iy⊗VolumeOperator(inner_stencil,closure_stencils,(10,),even)
154 @test op_x isa TensorMapping{T,3,3} where T
155 @test op_y isa TensorMapping{T,3,3} where T
156 @test op_z isa TensorMapping{T,3,3} where T
157 end
158 end
159
160 @testset "Sizes" begin
161 @testset "1D" begin
162 op = volume_operator(g_1D,inner_stencil,closure_stencils,even,1)
163 @test range_size(op) == domain_size(op) == size(g_1D)
164 end
165
166 @testset "2D" begin
167 op_x = volume_operator(g_2D,inner_stencil,closure_stencils,even,1)
168 op_y = volume_operator(g_2D,inner_stencil,closure_stencils,even,2)
169 @test range_size(op_y) == domain_size(op_y) ==
170 range_size(op_x) == domain_size(op_x) == size(g_2D)
171 end
172 @testset "3D" begin
173 op_x = volume_operator(g_3D,inner_stencil,closure_stencils,even,1)
174 op_y = volume_operator(g_3D,inner_stencil,closure_stencils,even,2)
175 op_z = volume_operator(g_3D,inner_stencil,closure_stencils,even,3)
176 @test range_size(op_z) == domain_size(op_z) ==
177 range_size(op_y) == domain_size(op_y) ==
178 range_size(op_x) == domain_size(op_x) == size(g_3D)
179 end
180 end
181
182 op_x = volume_operator(g_2D,inner_stencil,closure_stencils,even,1)
183 op_y = volume_operator(g_2D,inner_stencil,closure_stencils,odd,2)
184 v = zeros(size(g_2D))
185 Nx = size(g_2D)[1]
186 Ny = size(g_2D)[2]
187 for i = 1:Nx
188 v[i,:] .= i
189 end
190 rx = copy(v)
191 rx[1,:] .= 1.5
192 rx[Nx,:] .= (2*Nx-1)/2
193 ry = copy(v)
194 ry[:,Ny-1:Ny] = -v[:,Ny-1:Ny]
195
196 @testset "Application" begin
197 @test op_x*v ≈ rx rtol = 1e-14
198 @test op_y*v ≈ ry rtol = 1e-14
199 end
200
201 @testset "Regions" begin
202 @test (op_x*v)[Index(1,Lower),Index(3,Interior)] ≈ rx[1,3] rtol = 1e-14
203 @test (op_x*v)[Index(2,Lower),Index(3,Interior)] ≈ rx[2,3] rtol = 1e-14
204 @test (op_x*v)[Index(6,Interior),Index(3,Interior)] ≈ rx[6,3] rtol = 1e-14
205 @test (op_x*v)[Index(10,Upper),Index(3,Interior)] ≈ rx[10,3] rtol = 1e-14
206 @test (op_x*v)[Index(11,Upper),Index(3,Interior)] ≈ rx[11,3] rtol = 1e-14
207
208 @test_throws BoundsError (op_x*v)[Index(3,Lower),Index(3,Interior)]
209 @test_throws BoundsError (op_x*v)[Index(9,Upper),Index(3,Interior)]
210
211 @test (op_y*v)[Index(3,Interior),Index(1,Lower)] ≈ ry[3,1] rtol = 1e-14
212 @test (op_y*v)[Index(3,Interior),Index(2,Lower)] ≈ ry[3,2] rtol = 1e-14
213 @test (op_y*v)[Index(3,Interior),Index(6,Interior)] ≈ ry[3,6] rtol = 1e-14
214 @test (op_y*v)[Index(3,Interior),Index(11,Upper)] ≈ ry[3,11] rtol = 1e-14
215 @test (op_y*v)[Index(3,Interior),Index(12,Upper)] ≈ ry[3,12] rtol = 1e-14
216
217 @test_throws BoundsError (op_y*v)[Index(3,Interior),Index(10,Upper)]
218 @test_throws BoundsError (op_y*v)[Index(3,Interior),Index(3,Lower)]
219 end
220
221 @testset "Inferred" begin
222 @inferred apply(op_x, v,1,1)
223 @inferred apply(op_x, v, Index(1,Lower),Index(1,Lower))
224 @inferred apply(op_x, v, Index(6,Interior),Index(1,Lower))
225 @inferred apply(op_x, v, Index(11,Upper),Index(1,Lower))
226
227 @inferred apply(op_y, v,1,1)
228 @inferred apply(op_y, v, Index(1,Lower),Index(1,Lower))
229 @inferred apply(op_y, v, Index(1,Lower),Index(6,Interior))
230 @inferred apply(op_y, v, Index(1,Lower),Index(11,Upper))
231 end
232
233 end
234
235 @testset "SecondDerivative" begin
236 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
237 Lx = 3.5
238 Ly = 3.
239 g_1D = EquidistantGrid(121, 0.0, Lx)
240 g_2D = EquidistantGrid((121,123), (0.0, 0.0), (Lx, Ly))
241
242 @testset "Constructors" begin
243 @testset "1D" begin
244 Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
245 @test Dₓₓ == second_derivative(g_1D,op.innerStencil,op.closureStencils,1)
246 @test Dₓₓ isa VolumeOperator
247 end
248 @testset "2D" begin
249 Dₓₓ = second_derivative(g_2D,op.innerStencil,op.closureStencils,1)
250 D2 = second_derivative(g_1D,op.innerStencil,op.closureStencils)
251 I = IdentityMapping{Float64}(size(g_2D)[2])
252 @test Dₓₓ == D2⊗I
253 @test Dₓₓ isa TensorMapping{T,2,2} where T
254 end
255 end
256
257 # Exact differentiation is measured point-wise. In other cases
258 # the error is measured in the l2-norm.
259 @testset "Accuracy" begin
260 @testset "1D" begin
261 l2(v) = sqrt(spacing(g_1D)[1]*sum(v.^2));
262 monomials = ()
263 maxOrder = 4;
264 for i = 0:maxOrder-1
265 f_i(x) = 1/factorial(i)*x^i
266 monomials = (monomials...,evalOn(g_1D,f_i))
267 end
268 v = evalOn(g_1D,x -> sin(x))
269 vₓₓ = evalOn(g_1D,x -> -sin(x))
270
271 # 2nd order interior stencil, 1nd order boundary stencil,
272 # implies that L*v should be exact for monomials up to order 2.
273 @testset "2nd order" begin
274 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
275 Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
276 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
277 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
278 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
279 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-2 norm = l2
280 end
281
282 # 4th order interior stencil, 2nd order boundary stencil,
283 # implies that L*v should be exact for monomials up to order 3.
284 @testset "4th order" begin
285 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
286 Dₓₓ = second_derivative(g_1D,op.innerStencil,op.closureStencils)
287 # NOTE: high tolerances for checking the "exact" differentiation
288 # due to accumulation of round-off errors/cancellation errors?
289 @test Dₓₓ*monomials[1] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
290 @test Dₓₓ*monomials[2] ≈ zeros(Float64,size(g_1D)...) atol = 5e-10
291 @test Dₓₓ*monomials[3] ≈ monomials[1] atol = 5e-10
292 @test Dₓₓ*monomials[4] ≈ monomials[2] atol = 5e-10
293 @test Dₓₓ*v ≈ vₓₓ rtol = 5e-4 norm = l2
294 end
295 end
296
297 @testset "2D" begin
298 l2(v) = sqrt(prod(spacing(g_2D))*sum(v.^2));
299 binomials = ()
300 maxOrder = 4;
301 for i = 0:maxOrder-1
302 f_i(x,y) = 1/factorial(i)*y^i + x^i
303 binomials = (binomials...,evalOn(g_2D,f_i))
304 end
305 v = evalOn(g_2D, (x,y) -> sin(x)+cos(y))
306 v_yy = evalOn(g_2D,(x,y) -> -cos(y))
307
308 # 2nd order interior stencil, 1st order boundary stencil,
309 # implies that L*v should be exact for binomials up to order 2.
310 @testset "2nd order" begin
311 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
312 Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2)
313 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
314 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
315 @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
316 @test Dyy*v ≈ v_yy rtol = 5e-2 norm = l2
317 end
318
319 # 4th order interior stencil, 2nd order boundary stencil,
320 # implies that L*v should be exact for binomials up to order 3.
321 @testset "4th order" begin
322 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
323 Dyy = second_derivative(g_2D,op.innerStencil,op.closureStencils,2)
324 # NOTE: high tolerances for checking the "exact" differentiation
325 # due to accumulation of round-off errors/cancellation errors?
326 @test Dyy*binomials[1] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
327 @test Dyy*binomials[2] ≈ zeros(Float64,size(g_2D)...) atol = 5e-9
328 @test Dyy*binomials[3] ≈ evalOn(g_2D,(x,y)->1.) atol = 5e-9
329 @test Dyy*binomials[4] ≈ evalOn(g_2D,(x,y)->y) atol = 5e-9
330 @test Dyy*v ≈ v_yy rtol = 5e-4 norm = l2
331 end
332 end
333 end
334 end
335
336 @testset "Laplace" begin
337 g_1D = EquidistantGrid(101, 0.0, 1.)
338 g_3D = EquidistantGrid((51,101,52), (0.0, -1.0, 0.0), (1., 1., 1.))
339 @testset "Constructors" begin
340 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
341 @testset "1D" begin
342 L = laplace(g_1D, op.innerStencil, op.closureStencils)
343 @test L == second_derivative(g_1D, op.innerStencil, op.closureStencils)
344 @test L isa TensorMapping{T,1,1} where T
345 end
346 @testset "3D" begin
347 L = laplace(g_3D, op.innerStencil, op.closureStencils)
348 @test L isa TensorMapping{T,3,3} where T
349 Dxx = second_derivative(g_3D, op.innerStencil, op.closureStencils,1)
350 Dyy = second_derivative(g_3D, op.innerStencil, op.closureStencils,2)
351 Dzz = second_derivative(g_3D, op.innerStencil, op.closureStencils,3)
352 @test L == Dxx + Dyy + Dzz
353 end
354 end
355
356 # Exact differentiation is measured point-wise. In other cases
357 # the error is measured in the l2-norm.
358 @testset "Accuracy" begin
359 l2(v) = sqrt(prod(spacing(g_3D))*sum(v.^2));
360 polynomials = ()
361 maxOrder = 4;
362 for i = 0:maxOrder-1
363 f_i(x,y,z) = 1/factorial(i)*(y^i + x^i + z^i)
364 polynomials = (polynomials...,evalOn(g_3D,f_i))
365 end
366 v = evalOn(g_3D, (x,y,z) -> sin(x) + cos(y) + exp(z))
367 Δv = evalOn(g_3D,(x,y,z) -> -sin(x) - cos(y) + exp(z))
368
369 # 2nd order interior stencil, 1st order boundary stencil,
370 # implies that L*v should be exact for binomials up to order 2.
371 @testset "2nd order" begin
372 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
373 L = laplace(g_3D,op.innerStencil,op.closureStencils)
374 @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
375 @test L*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
376 @test L*polynomials[3] ≈ polynomials[1] atol = 5e-9
377 @test L*v ≈ Δv rtol = 5e-2 norm = l2
378 end
379
380 # 4th order interior stencil, 2nd order boundary stencil,
381 # implies that L*v should be exact for binomials up to order 3.
382 @testset "4th order" begin
383 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
384 L = laplace(g_3D,op.innerStencil,op.closureStencils)
385 # NOTE: high tolerances for checking the "exact" differentiation
386 # due to accumulation of round-off errors/cancellation errors?
387 @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
388 @test L*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
389 @test L*polynomials[3] ≈ polynomials[1] atol = 5e-9
390 @test L*polynomials[4] ≈ polynomials[2] atol = 5e-9
391 @test L*v ≈ Δv rtol = 5e-4 norm = l2
392 end
393 end
394 end
395
396 @testset "Diagonal-stencil inner_product" begin
397 Lx = π/2.
398 Ly = Float64(π)
399 Lz = 1.
400 g_1D = EquidistantGrid(77, 0.0, Lx)
401 g_2D = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
402 g_3D = EquidistantGrid((10,10, 10), (0.0, 0.0, 0.0), (Lx,Ly,Lz))
403 integral(H,v) = sum(H*v)
404 @testset "inner_product" begin
405 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
406 @testset "0D" begin
407 H = inner_product(EquidistantGrid{Float64}(),op.quadratureClosure)
408 @test H == IdentityMapping{Float64}()
409 @test H isa TensorMapping{T,0,0} where T
410 end
411 @testset "1D" begin
412 H = inner_product(g_1D,op.quadratureClosure)
413 inner_stencil = CenteredStencil(1.)
414 @test H == inner_product(g_1D,op.quadratureClosure,inner_stencil)
415 @test H isa TensorMapping{T,1,1} where T
416 end
417 @testset "2D" begin
418 H = inner_product(g_2D,op.quadratureClosure)
419 H_x = inner_product(restrict(g_2D,1),op.quadratureClosure)
420 H_y = inner_product(restrict(g_2D,2),op.quadratureClosure)
421 @test H == H_x⊗H_y
422 @test H isa TensorMapping{T,2,2} where T
423 end
424 end
425
426 @testset "Sizes" begin
427 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
428 @testset "1D" begin
429 H = inner_product(g_1D,op.quadratureClosure)
430 @test domain_size(H) == size(g_1D)
431 @test range_size(H) == size(g_1D)
432 end
433 @testset "2D" begin
434 H = inner_product(g_2D,op.quadratureClosure)
435 @test domain_size(H) == size(g_2D)
436 @test range_size(H) == size(g_2D)
437 end
438 end
439
440 @testset "Accuracy" begin
441 @testset "1D" begin
442 v = ()
443 for i = 0:4
444 f_i(x) = 1/factorial(i)*x^i
445 v = (v...,evalOn(g_1D,f_i))
446 end
447 u = evalOn(g_1D,x->sin(x))
448
449 @testset "2nd order" begin
450 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
451 H = inner_product(g_1D,op.quadratureClosure)
452 for i = 1:2
453 @test integral(H,v[i]) ≈ v[i+1][end] - v[i+1][1] rtol = 1e-14
454 end
455 @test integral(H,u) ≈ 1. rtol = 1e-4
456 end
457
458 @testset "4th order" begin
459 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
460 H = inner_product(g_1D,op.quadratureClosure)
461 for i = 1:4
462 @test integral(H,v[i]) ≈ v[i+1][end] - v[i+1][1] rtol = 1e-14
463 end
464 @test integral(H,u) ≈ 1. rtol = 1e-8
465 end
466 end
467
468 @testset "2D" begin
469 b = 2.1
470 v = b*ones(Float64, size(g_2D))
471 u = evalOn(g_2D,(x,y)->sin(x)+cos(y))
472 @testset "2nd order" begin
473 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
474 H = inner_product(g_2D,op.quadratureClosure)
475 @test integral(H,v) ≈ b*Lx*Ly rtol = 1e-13
476 @test integral(H,u) ≈ π rtol = 1e-4
477 end
478 @testset "4th order" begin
479 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
480 H = inner_product(g_2D,op.quadratureClosure)
481 @test integral(H,v) ≈ b*Lx*Ly rtol = 1e-13
482 @test integral(H,u) ≈ π rtol = 1e-8
483 end
484 end
485 end
486 end
487
488 @testset "Diagonal-stencil inverse_inner_product" begin
489 Lx = π/2.
490 Ly = Float64(π)
491 g_1D = EquidistantGrid(77, 0.0, Lx)
492 g_2D = EquidistantGrid((77,66), (0.0, 0.0), (Lx,Ly))
493 @testset "inverse_inner_product" begin
494 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
495 @testset "0D" begin
496 Hi = inverse_inner_product(EquidistantGrid{Float64}(),op.quadratureClosure)
497 @test Hi == IdentityMapping{Float64}()
498 @test Hi isa TensorMapping{T,0,0} where T
499 end
500 @testset "1D" begin
501 Hi = inverse_inner_product(g_1D, op.quadratureClosure);
502 inner_stencil = CenteredStencil(1.)
503 closures = ()
504 for i = 1:length(op.quadratureClosure)
505 closures = (closures...,Stencil(op.quadratureClosure[i].range,1.0./op.quadratureClosure[i].weights))
506 end
507 @test Hi == inverse_inner_product(g_1D,closures,inner_stencil)
508 @test Hi isa TensorMapping{T,1,1} where T
509 end
510 @testset "2D" begin
511 Hi = inverse_inner_product(g_2D,op.quadratureClosure)
512 Hi_x = inverse_inner_product(restrict(g_2D,1),op.quadratureClosure)
513 Hi_y = inverse_inner_product(restrict(g_2D,2),op.quadratureClosure)
514 @test Hi == Hi_x⊗Hi_y
515 @test Hi isa TensorMapping{T,2,2} where T
516 end
517 end
518
519 @testset "Sizes" begin
520 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
521 @testset "1D" begin
522 Hi = inverse_inner_product(g_1D,op.quadratureClosure)
523 @test domain_size(Hi) == size(g_1D)
524 @test range_size(Hi) == size(g_1D)
525 end
526 @testset "2D" begin
527 Hi = inverse_inner_product(g_2D,op.quadratureClosure)
528 @test domain_size(Hi) == size(g_2D)
529 @test range_size(Hi) == size(g_2D)
530 end
531 end
532
533 @testset "Accuracy" begin
534 @testset "1D" begin
535 v = evalOn(g_1D,x->sin(x))
536 u = evalOn(g_1D,x->x^3-x^2+1)
537 @testset "2nd order" begin
538 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
539 H = inner_product(g_1D,op.quadratureClosure)
540 Hi = inverse_inner_product(g_1D,op.quadratureClosure)
541 @test Hi*H*v ≈ v rtol = 1e-15
542 @test Hi*H*u ≈ u rtol = 1e-15
543 end
544 @testset "4th order" begin
545 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
546 H = inner_product(g_1D,op.quadratureClosure)
547 Hi = inverse_inner_product(g_1D,op.quadratureClosure)
548 @test Hi*H*v ≈ v rtol = 1e-15
549 @test Hi*H*u ≈ u rtol = 1e-15
550 end
551 end
552 @testset "2D" begin
553 v = evalOn(g_2D,(x,y)->sin(x)+cos(y))
554 u = evalOn(g_2D,(x,y)->x*y + x^5 - sqrt(y))
555 @testset "2nd order" begin
556 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
557 H = inner_product(g_2D,op.quadratureClosure)
558 Hi = inverse_inner_product(g_2D,op.quadratureClosure)
559 @test Hi*H*v ≈ v rtol = 1e-15
560 @test Hi*H*u ≈ u rtol = 1e-15
561 end
562 @testset "4th order" begin
563 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
564 H = inner_product(g_2D,op.quadratureClosure)
565 Hi = inverse_inner_product(g_2D,op.quadratureClosure)
566 @test Hi*H*v ≈ v rtol = 1e-15
567 @test Hi*H*u ≈ u rtol = 1e-15
568 end
569 end
570 end
571 end
572
573 @testset "BoundaryOperator" begin
574 closure_stencil = Stencil((0,2), (2.,1.,3.))
575 g_1D = EquidistantGrid(11, 0.0, 1.0)
576 g_2D = EquidistantGrid((11,15), (0.0, 0.0), (1.0,1.0))
577
578 @testset "Constructors" begin
579 @testset "1D" begin
580 op_l = BoundaryOperator{Lower}(closure_stencil,size(g_1D)[1])
581 @test op_l == BoundaryOperator(g_1D,closure_stencil,Lower())
582 @test op_l == boundary_operator(g_1D,closure_stencil,CartesianBoundary{1,Lower}())
583 @test op_l isa TensorMapping{T,0,1} where T
584
585 op_r = BoundaryOperator{Upper}(closure_stencil,size(g_1D)[1])
586 @test op_r == BoundaryOperator(g_1D,closure_stencil,Upper())
587 @test op_r == boundary_operator(g_1D,closure_stencil,CartesianBoundary{1,Upper}())
588 @test op_r isa TensorMapping{T,0,1} where T
589 end
590
591 @testset "2D" begin
592 e_w = boundary_operator(g_2D,closure_stencil,CartesianBoundary{1,Upper}())
593 @test e_w isa InflatedTensorMapping
594 @test e_w isa TensorMapping{T,1,2} where T
595 end
596 end
597
598 op_l = boundary_operator(g_1D, closure_stencil, CartesianBoundary{1,Lower}())
599 op_r = boundary_operator(g_1D, closure_stencil, CartesianBoundary{1,Upper}())
600
601 op_w = boundary_operator(g_2D, closure_stencil, CartesianBoundary{1,Lower}())
602 op_e = boundary_operator(g_2D, closure_stencil, CartesianBoundary{1,Upper}())
603 op_s = boundary_operator(g_2D, closure_stencil, CartesianBoundary{2,Lower}())
604 op_n = boundary_operator(g_2D, closure_stencil, CartesianBoundary{2,Upper}())
605
606 @testset "Sizes" begin
607 @testset "1D" begin
608 @test domain_size(op_l) == (11,)
609 @test domain_size(op_r) == (11,)
610
611 @test range_size(op_l) == ()
612 @test range_size(op_r) == ()
613 end
614
615 @testset "2D" begin
616 @test domain_size(op_w) == (11,15)
617 @test domain_size(op_e) == (11,15)
618 @test domain_size(op_s) == (11,15)
619 @test domain_size(op_n) == (11,15)
620
621 @test range_size(op_w) == (15,)
622 @test range_size(op_e) == (15,)
623 @test range_size(op_s) == (11,)
624 @test range_size(op_n) == (11,)
625 end
626 end
627
628 @testset "Application" begin
629 @testset "1D" begin
630 v = evalOn(g_1D,x->1+x^2)
631 u = fill(3.124)
632 @test (op_l*v)[] == 2*v[1] + v[2] + 3*v[3]
633 @test (op_r*v)[] == 2*v[end] + v[end-1] + 3*v[end-2]
634 @test (op_r*v)[1] == 2*v[end] + v[end-1] + 3*v[end-2]
635 @test op_l'*u == [2*u[]; u[]; 3*u[]; zeros(8)]
636 @test op_r'*u == [zeros(8); 3*u[]; u[]; 2*u[]]
637 end
638
639 @testset "2D" begin
640 v = rand(size(g_2D)...)
641 u = fill(3.124)
642 @test op_w*v ≈ 2*v[1,:] + v[2,:] + 3*v[3,:] rtol = 1e-14
643 @test op_e*v ≈ 2*v[end,:] + v[end-1,:] + 3*v[end-2,:] rtol = 1e-14
644 @test op_s*v ≈ 2*v[:,1] + v[:,2] + 3*v[:,3] rtol = 1e-14
645 @test op_n*v ≈ 2*v[:,end] + v[:,end-1] + 3*v[:,end-2] rtol = 1e-14
646
647
648 g_x = rand(size(g_2D)[1])
649 g_y = rand(size(g_2D)[2])
650
651 G_w = zeros(Float64, size(g_2D)...)
652 G_w[1,:] = 2*g_y
653 G_w[2,:] = g_y
654 G_w[3,:] = 3*g_y
655
656 G_e = zeros(Float64, size(g_2D)...)
657 G_e[end,:] = 2*g_y
658 G_e[end-1,:] = g_y
659 G_e[end-2,:] = 3*g_y
660
661 G_s = zeros(Float64, size(g_2D)...)
662 G_s[:,1] = 2*g_x
663 G_s[:,2] = g_x
664 G_s[:,3] = 3*g_x
665
666 G_n = zeros(Float64, size(g_2D)...)
667 G_n[:,end] = 2*g_x
668 G_n[:,end-1] = g_x
669 G_n[:,end-2] = 3*g_x
670
671 @test op_w'*g_y == G_w
672 @test op_e'*g_y == G_e
673 @test op_s'*g_x == G_s
674 @test op_n'*g_x == G_n
675 end
676
677 @testset "Regions" begin
678 u = fill(3.124)
679 @test (op_l'*u)[Index(1,Lower)] == 2*u[]
680 @test (op_l'*u)[Index(2,Lower)] == u[]
681 @test (op_l'*u)[Index(6,Interior)] == 0
682 @test (op_l'*u)[Index(10,Upper)] == 0
683 @test (op_l'*u)[Index(11,Upper)] == 0
684
685 @test (op_r'*u)[Index(1,Lower)] == 0
686 @test (op_r'*u)[Index(2,Lower)] == 0
687 @test (op_r'*u)[Index(6,Interior)] == 0
688 @test (op_r'*u)[Index(10,Upper)] == u[]
689 @test (op_r'*u)[Index(11,Upper)] == 2*u[]
690 end
691 end
692
693 @testset "Inferred" begin
694 v = ones(Float64, 11)
695 u = fill(1.)
696
697 @inferred apply(op_l, v)
698 @inferred apply(op_r, v)
699
700 @inferred apply_transpose(op_l, u, 4)
701 @inferred apply_transpose(op_l, u, Index(1,Lower))
702 @inferred apply_transpose(op_l, u, Index(2,Lower))
703 @inferred apply_transpose(op_l, u, Index(6,Interior))
704 @inferred apply_transpose(op_l, u, Index(10,Upper))
705 @inferred apply_transpose(op_l, u, Index(11,Upper))
706
707 @inferred apply_transpose(op_r, u, 4)
708 @inferred apply_transpose(op_r, u, Index(1,Lower))
709 @inferred apply_transpose(op_r, u, Index(2,Lower))
710 @inferred apply_transpose(op_r, u, Index(6,Interior))
711 @inferred apply_transpose(op_r, u, Index(10,Upper))
712 @inferred apply_transpose(op_r, u, Index(11,Upper))
713 end
714
715 end
716
717 @testset "boundary_restriction" begin
718 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
719 g_1D = EquidistantGrid(11, 0.0, 1.0)
720 g_2D = EquidistantGrid((11,15), (0.0, 0.0), (1.0,1.0))
721
722 @testset "boundary_restriction" begin
723 @testset "1D" begin
724 e_l = boundary_restriction(g_1D,op.eClosure,Lower())
725 @test e_l == boundary_restriction(g_1D,op.eClosure,CartesianBoundary{1,Lower}())
726 @test e_l == BoundaryOperator(g_1D,op.eClosure,Lower())
727 @test e_l isa BoundaryOperator{T,Lower} where T
728 @test e_l isa TensorMapping{T,0,1} where T
729
730 e_r = boundary_restriction(g_1D,op.eClosure,Upper())
731 @test e_r == boundary_restriction(g_1D,op.eClosure,CartesianBoundary{1,Upper}())
732 @test e_r == BoundaryOperator(g_1D,op.eClosure,Upper())
733 @test e_r isa BoundaryOperator{T,Upper} where T
734 @test e_r isa TensorMapping{T,0,1} where T
735 end
736
737 @testset "2D" begin
738 e_w = boundary_restriction(g_2D,op.eClosure,CartesianBoundary{1,Upper}())
739 @test e_w isa InflatedTensorMapping
740 @test e_w isa TensorMapping{T,1,2} where T
741 end
742 end
743
744 @testset "Application" begin
745 @testset "1D" begin
746 e_l = boundary_restriction(g_1D, op.eClosure, CartesianBoundary{1,Lower}())
747 e_r = boundary_restriction(g_1D, op.eClosure, CartesianBoundary{1,Upper}())
748
749 v = evalOn(g_1D,x->1+x^2)
750 u = fill(3.124)
751
752 @test (e_l*v)[] == v[1]
753 @test (e_r*v)[] == v[end]
754 @test (e_r*v)[1] == v[end]
755 end
756
757 @testset "2D" begin
758 e_w = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{1,Lower}())
759 e_e = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{1,Upper}())
760 e_s = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{2,Lower}())
761 e_n = boundary_restriction(g_2D, op.eClosure, CartesianBoundary{2,Upper}())
762
763 v = rand(11, 15)
764 u = fill(3.124)
765
766 @test e_w*v == v[1,:]
767 @test e_e*v == v[end,:]
768 @test e_s*v == v[:,1]
769 @test e_n*v == v[:,end]
770 end
771 end
772 end
773
774 @testset "normal_derivative" begin
775 g_1D = EquidistantGrid(11, 0.0, 1.0)
776 g_2D = EquidistantGrid((11,12), (0.0, 0.0), (1.0,1.0))
777 @testset "normal_derivative" begin
778 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
779 @testset "1D" begin
780 d_l = normal_derivative(g_1D, op.dClosure, Lower())
781 @test d_l == normal_derivative(g_1D, op.dClosure, CartesianBoundary{1,Lower}())
782 @test d_l isa BoundaryOperator{T,Lower} where T
783 @test d_l isa TensorMapping{T,0,1} where T
784 end
785 @testset "2D" begin
786 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
787 d_w = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Lower}())
788 d_n = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Upper}())
789 Ix = IdentityMapping{Float64}((size(g_2D)[1],))
790 Iy = IdentityMapping{Float64}((size(g_2D)[2],))
791 d_l = normal_derivative(restrict(g_2D,1),op.dClosure,Lower())
792 d_r = normal_derivative(restrict(g_2D,2),op.dClosure,Upper())
793 @test d_w == d_l⊗Iy
794 @test d_n == Ix⊗d_r
795 @test d_w isa TensorMapping{T,1,2} where T
796 @test d_n isa TensorMapping{T,1,2} where T
797 end
798 end
799 @testset "Accuracy" begin
800 v = evalOn(g_2D, (x,y)-> x^2 + (y-1)^2 + x*y)
801 v∂x = evalOn(g_2D, (x,y)-> 2*x + y)
802 v∂y = evalOn(g_2D, (x,y)-> 2*(y-1) + x)
803 # TODO: Test for higher order polynomials?
804 @testset "2nd order" begin
805 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=2)
806 d_w = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Lower}())
807 d_e = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Upper}())
808 d_s = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Lower}())
809 d_n = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Upper}())
810
811 @test d_w*v ≈ v∂x[1,:] atol = 1e-13
812 @test d_e*v ≈ -v∂x[end,:] atol = 1e-13
813 @test d_s*v ≈ v∂y[:,1] atol = 1e-13
814 @test d_n*v ≈ -v∂y[:,end] atol = 1e-13
815 end
816
817 @testset "4th order" begin
818 op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
819 d_w = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Lower}())
820 d_e = normal_derivative(g_2D, op.dClosure, CartesianBoundary{1,Upper}())
821 d_s = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Lower}())
822 d_n = normal_derivative(g_2D, op.dClosure, CartesianBoundary{2,Upper}())
823
824 @test d_w*v ≈ v∂x[1,:] atol = 1e-13
825 @test d_e*v ≈ -v∂x[end,:] atol = 1e-13
826 @test d_s*v ≈ v∂y[:,1] atol = 1e-13
827 @test d_n*v ≈ -v∂y[:,end] atol = 1e-13
828 end
829 end
830 end
831
832 end