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Add tests for SBP property #272

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merged 2 commits into from
Jun 16, 2024
Merged

Add tests for SBP property #272

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dd4c1b9
add tests for SBP property
JoshuaLampert Jun 16, 2024
bca68a5
Merge branch 'main' into test-SBP-property
ranocha Jun 16, 2024
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37 changes: 37 additions & 0 deletions test/SBP_operators_test.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -16,6 +16,9 @@ for source in D_test_list, T in (Float32,Float64)
xmin = -one(T)
xmax = 2*one(T)
N = 101
B = zeros(T, N, N)
B[1, 1] = convert(T, -1)
B[end, end] = convert(T, 1)
der_order = 1

acc_order = 2
Expand All @@ -42,6 +45,9 @@ for source in D_test_list, T in (Float32,Float64)
@test issymmetric(D) == false
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
# SBP property
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ B
# interior and boundary
mul!(res, D, x0)
@test all(i->abs(res[i]) < 1000*eps(T), eachindex(res))
Expand Down Expand Up @@ -88,6 +94,9 @@ for source in D_test_list, T in (Float32,Float64)
@test issymmetric(D) == false
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
# SBP property
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ B
# interior and boundary
mul!(res, D, x0)
@test all(i->abs(res[i]) < 1000*eps(T), eachindex(res))
Expand Down Expand Up @@ -142,6 +151,9 @@ for source in D_test_list, T in (Float32,Float64)
@test issymmetric(D) == false
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
# SBP property
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ B
# interior and boundary
mul!(res, D, x0)
@test all(i->abs(res[i]) < 1000*eps(T), eachindex(res))
Expand Down Expand Up @@ -202,6 +214,9 @@ for source in D_test_list, T in (Float32,Float64)
@test issymmetric(D) == false
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
# SBP property
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ B
# interior and boundary
mul!(res, D, x0)
@test all(i->abs(res[i]) < 16000*eps(T), eachindex(res))
Expand Down Expand Up @@ -241,6 +256,8 @@ for source in D_test_list, T in (Float32,Float64)
xmin = -one(T)
xmax = 2*one(T)
N = 101
eL = SummationByPartsOperators.OneHot(1, N)
eR = SummationByPartsOperators.OneHot(N, N)
der_order = 2

acc_order = 2
Expand All @@ -267,6 +284,11 @@ for source in D_test_list, T in (Float32,Float64)
@test issymmetric(D) == false
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
# SBP property
M = mass_matrix(D)
dL = derivative_left(D, Val{1}())
dR = derivative_right(D, Val{1}())
@test M * Matrix(D) - Matrix(D)' * M ≈ eR * dR' - eL * dL' - dR * eR' + dL * eL'
# interior and boundary
mul!(res, D, x0)
@test all(i->abs(res[i]) < eps(T), eachindex(res))
Expand Down Expand Up @@ -315,6 +337,11 @@ for source in D_test_list, T in (Float32,Float64)
@test issymmetric(D) == false
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
# SBP property
M = mass_matrix(D)
dL = derivative_left(D, Val{1}())
dR = derivative_right(D, Val{1}())
@test M * Matrix(D) - Matrix(D)' * M ≈ eR * dR' - eL * dL' - dR * eR' + dL * eL'
# interior and boundary
mul!(res, D, x0)
@test all(i->abs(res[i]) < 2000*eps(T), eachindex(res))
Expand Down Expand Up @@ -369,6 +396,11 @@ for source in D_test_list, T in (Float32,Float64)
@test issymmetric(D) == false
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
# SBP property
M = mass_matrix(D)
dL = derivative_left(D, Val{1}())
dR = derivative_right(D, Val{1}())
@test M * Matrix(D) - Matrix(D)' * M ≈ eR * dR' - eL * dL' - dR * eR' + dL * eL'
# interior and boundary
mul!(res, D, x0)
@test all(i->abs(res[i]) < 10000*eps(T), eachindex(res))
Expand Down Expand Up @@ -428,6 +460,11 @@ for source in D_test_list, T in (Float32,Float64)
@test issymmetric(D) == false
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
# SBP property
M = mass_matrix(D)
dL = derivative_left(D, Val{1}())
dR = derivative_right(D, Val{1}())
@test M * Matrix(D) - Matrix(D)' * M ≈ eR * dR' - eL * dL' - dR * eR' + dL * eL'
# interior and boundary
mul!(res, D, x0)
@test all(i->abs(res[i]) < 10000*eps(T), eachindex(res))
Expand Down
2 changes: 2 additions & 0 deletions test/fourier_operators_test.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -21,6 +21,8 @@ for T in (Float32, Float64)
@test issymmetric(D) == false
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
M = mass_matrix(D)
@test isapprox(M * Matrix(D) + Matrix(D)' * M, zeros(T, N, N), atol = N*eps(T))
u = compute_coefficients(zero, D)
res = D*u
for k in 0:(N÷2)-1
Expand Down
5 changes: 5 additions & 0 deletions test/legendre_operators_test.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -16,13 +16,18 @@ for T in (Float32, Float64)
xmax = one(T)

for N in 2 .^ (1:4)
B = zeros(T, N, N)
B[1, 1] = convert(T, -1)
B[end, end] = convert(T, 1)
D = legendre_derivative_operator(xmin, xmax, N)
@test D == legendre_derivative_operator(xmin=xmin, xmax=xmax, N=N)
println(devnull, D)
@test SummationByPartsOperators.derivative_order(D) == 1
@test issymmetric(D) == false
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ B
u = compute_coefficients(zero, D)
res = D*u
for k in 1:N-1
Expand Down
47 changes: 44 additions & 3 deletions test/periodic_operators_test.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -31,6 +31,8 @@ let T=Float32
@test issymmetric(D) == false
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0)
@test all(i->abs(res[i]) < eps(T), accuracy_order:length(res)-accuracy_order)
mul!(res, D, x1)
Expand All @@ -48,6 +50,8 @@ let T=Float32
@test issymmetric(D) == false
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0)
@test all(i->abs(res[i]) < 50*eps(T), accuracy_order:length(res)-accuracy_order)
mul!(res, D, x1)
Expand All @@ -69,6 +73,8 @@ let T=Float32
@test issymmetric(D) == false
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0)
@test all(i->abs(res[i]) < 50*eps(T), accuracy_order:length(res)-accuracy_order)
mul!(res, D, x1)
Expand Down Expand Up @@ -96,6 +102,8 @@ let T=Float32
@test issymmetric(D) == true
@test SummationByPartsOperators.xmin(D) ≈ xmin
@test SummationByPartsOperators.xmax(D) ≈ xmax
M = mass_matrix(D)
@test M * Matrix(D) - Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0)
@test all(i->abs(res[i]) < eps(T), accuracy_order:length(res)-accuracy_order)
mul!(res, D, x1)
Expand All @@ -115,6 +123,8 @@ let T=Float32
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == true
M = mass_matrix(D)
@test M * Matrix(D) - Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0)
@test all(i->abs(res[i]) < 50N*eps(T), accuracy_order:length(res)-accuracy_order)
mul!(res, D, x1)
Expand All @@ -136,6 +146,8 @@ let T=Float32
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == true
M = mass_matrix(D)
@test M * Matrix(D) - Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 50N*eps(T)
mul!(res, D, x1); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 1000N*eps(T)
mul!(res, D, x2); @test norm((res - 2 .* x0)[accuracy_order:end-accuracy_order], Inf) < 5000N*eps(T)
Expand All @@ -159,6 +171,8 @@ let T=Float32
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == true # because this operator is zero!
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0); @test norm(res[accuracy_order:end-accuracy_order], Inf) < eps(T)
mul!(res, D, x1); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 1400*eps(T)
mul!(res, D, x2); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 7000*eps(T)
Expand All @@ -172,6 +186,8 @@ let T=Float32
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == false
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 400*eps(T)
mul!(res, D, x1); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 10000N*eps(T)
mul!(res, D, x2); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 50000N*eps(T)
Expand All @@ -187,6 +203,8 @@ let T=Float32
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == false
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 300*eps(T)
mul!(res, D, x1); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 80000N*eps(T)
mul!(res, D, x2); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 300000N*eps(T)
Expand Down Expand Up @@ -237,6 +255,8 @@ let T = Float64
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == false
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0)
@test all(i->abs(res[i]) < eps(T), accuracy_order:length(res)-accuracy_order)
mul!(res, D, x1)
Expand All @@ -252,9 +272,8 @@ let T = Float64
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == false
accuracy_order = 4
D = periodic_central_derivative_operator(1, accuracy_order, xmin, xmax, N)
@test issymmetric(D) == false
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M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0)
@test all(i->abs(res[i]) < 10*eps(T), accuracy_order:length(res)-accuracy_order)
mul!(res, D, x1)
Expand All @@ -274,6 +293,8 @@ let T = Float64
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == false
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0)
@test all(i->abs(res[i]) < 10*eps(T), accuracy_order:length(res)-accuracy_order)
mul!(res, D, x1)
Expand Down Expand Up @@ -303,6 +324,8 @@ let T = Float64
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == true
M = mass_matrix(D)
@test M * Matrix(D) - Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0); @test norm(res[accuracy_order:end-accuracy_order], Inf) < eps(T)
mul!(res, D, x1); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 1400*eps(T)
mul!(res, D, x2); @test norm((res - 2 .* x0)[accuracy_order:end-accuracy_order], Inf) < 7000*eps(T)
Expand All @@ -314,6 +337,8 @@ let T = Float64
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == true
M = mass_matrix(D)
@test M * Matrix(D) - Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 400*eps(T)
mul!(res, D, x1); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 5000*eps(T)
mul!(res, D, x2); @test norm((res - 2 .* x0)[accuracy_order:end-accuracy_order], Inf) < 11000*eps(T)
Expand All @@ -327,6 +352,8 @@ let T = Float64
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == true
M = mass_matrix(D)
@test M * Matrix(D) - Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 1000*eps(T)
mul!(res, D, x1); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 5000*eps(T)
mul!(res, D, x2); @test norm((res - 2 .* x0)[accuracy_order:end-accuracy_order], Inf) < 10020*eps(T)
Expand All @@ -348,6 +375,8 @@ let T = Float64
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == true # because this operator is zero!
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0); @test norm(res[accuracy_order:end-accuracy_order], Inf) < eps(T)
mul!(res, D, x1); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 1400*eps(T)
mul!(res, D, x2); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 7000*eps(T)
Expand All @@ -359,6 +388,8 @@ let T = Float64
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == false
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 400*eps(T)
mul!(res, D, x1); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 20000*eps(T)
mul!(res, D, x2); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 200000*eps(T)
Expand All @@ -372,6 +403,8 @@ let T = Float64
@test SummationByPartsOperators.derivative_order(D) == derivative_order
@test SummationByPartsOperators.accuracy_order(D) == accuracy_order
@test issymmetric(D) == false
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 300*eps(T)
mul!(res, D, x1); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 70000*eps(T)
mul!(res, D, x2); @test norm(res[accuracy_order:end-accuracy_order], Inf) < 200000*eps(T)
Expand Down Expand Up @@ -718,6 +751,8 @@ let T = Float32
@test derivative_order(D) == der_order
@test accuracy_order(D) == acc_order
@test issymmetric(D) == false
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0)
@test all(i->abs(res[i]) < eps(T), stencil_width:length(res)-stencil_width)
mul!(res, D, x1)
Expand All @@ -738,6 +773,8 @@ let T = Float32
@test derivative_order(D) == der_order
@test accuracy_order(D) == acc_order
@test issymmetric(D) == false
M = mass_matrix(D)
@test M * Matrix(D) + Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0)
@test all(i->abs(res[i]) < 50*eps(T), stencil_width:length(res)-stencil_width)
mul!(res, D, x1)
Expand Down Expand Up @@ -770,6 +807,8 @@ let T = Float32
@test derivative_order(D) == der_order
@test accuracy_order(D) == acc_order
@test issymmetric(D) == true
M = mass_matrix(D)
@test M * Matrix(D) - Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0)
@test all(i->abs(res[i]) < eps(T), stencil_width:length(res)-stencil_width)
mul!(res, D, x1)
Expand All @@ -792,6 +831,8 @@ let T = Float32
@test derivative_order(D) == der_order
@test accuracy_order(D) == acc_order
@test issymmetric(D) == true
M = mass_matrix(D)
@test M * Matrix(D) - Matrix(D)' * M ≈ zeros(T, N, N)
mul!(res, D, x0)
@test all(i->abs(res[i]) < 50N*eps(T), stencil_width:length(res)-stencil_width)
mul!(res, D, x1)
Expand Down
7 changes: 6 additions & 1 deletion test/upwind_operators_test.jl
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Expand Up @@ -63,7 +63,6 @@ end
N = 21
xmin = 0.
xmax = Float64(N + 1)
interior = 10:N-10
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acc_order = 2

D = upwind_operators(Mattsson2017, derivative_order=1, accuracy_order=acc_order,
Expand Down Expand Up @@ -97,6 +96,12 @@ end
x = grid(D)
@test integrate(x, D) == integrate(x, Dp)

B = zeros(N, N)
B[1, 1] = -1.0
B[end, end] = 1.0
M = mass_matrix(D)
@test M * Matrix(Dp) + Matrix(Dm)' * M ≈ B

@test_throws ArgumentError UpwindOperators(
derivative_operator(Mattsson2017(:minus ), 1, acc_order, xmin, xmax, N),
derivative_operator(Mattsson2017(:central), 1, acc_order, xmin, xmax, N+1),
Expand Down
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