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| using LinearAlgebra | ||
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| # order 2 | ||
| Qp = [ | ||
| -1//4 5//4 -1//2 0 0 0 | ||
| -1//4 -5//4 2 -1//2 0 0 | ||
| 0 0 -3//2 2 -1//2 0 | ||
| 0 0 0 -3//2 2 -1//2 | ||
| 0 0 0 0 -5//4 5//4 | ||
| 0 0 0 0 -1//4 -1//4 | ||
| ] | ||
| Qm = Matrix(-Qp') | ||
| B = zero(Qp); B[1,1] = -1; B[end,end] = 1 | ||
| M = Diagonal([1//4, 5//4, 1, 1, 5//4, 1//4]) | ||
| Dp = M \ (Qp + B / 2) | ||
| Dm = M \ (Qm + B / 2) | ||
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| # order 3 | ||
| Qp = [ | ||
| -1//12 3//4 -1//6 0 0 0 | ||
| -5//12 -5//12 1 -1//6 0 0 | ||
| 0 -1//3 -1//2 1 -1//6 0 | ||
| 0 0 -1//3 -1//2 1 -1//6 | ||
| 0 0 0 -1//3 -5//12 3//4 | ||
| 0 0 0 0 -5//12 -1//12 | ||
| ] | ||
| Qm = Matrix(-Qp') | ||
| B = zero(Qp); B[1,1] = -1; B[end,end] = 1 | ||
| M = Diagonal([5//12, 13//12, 1, 1, 13//12, 5//12]) | ||
| Dp = M \ (Qp + B / 2) | ||
| Dm = M \ (Qm + B / 2) | ||
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| # order 4 | ||
| Qp = [ | ||
| -1//48 205//288 -29//144 1//96 0 0 0 0 0 0 0 | ||
| -169//288 -11//48 33//32 -43//144 1//12 0 0 0 0 0 0 | ||
| 11//144 -13//32 -29//48 389//288 -1//2 1//12 0 0 0 0 0 | ||
| 1//32 -11//144 -65//288 -13//16 3//2 -1//2 1//12 0 0 0 0 | ||
| 0 0 0 -1//4 -5//6 3//2 -1//2 1//12 0 0 0 | ||
| 0 0 0 0 -1//4 -5//6 3//2 -1//2 1//12 0 0 | ||
| 0 0 0 0 0 -1//4 -5//6 3//2 -1//2 1//12 0 | ||
| 0 0 0 0 0 0 -1//4 -13//16 389//288 -43//144 1//96 | ||
| 0 0 0 0 0 0 0 -65//288 -29//48 33//32 -29//144 | ||
| 0 0 0 0 0 0 0 -11//144 -13//32 -11//48 205//288 | ||
| 0 0 0 0 0 0 0 1//32 11//144 -169//288 -1//48 | ||
| ] | ||
| Qm = Matrix(-Qp') | ||
| B = zero(Qp); B[1,1] = -1; B[end,end] = 1 | ||
| m = [49//144, 61//48, 41//48, 149//144] | ||
| M = Diagonal(vcat(m, ones(Int, size(Qp,1)-2*length(m)), m[end:-1:1])) | ||
| Dp = M \ (Qp + B / 2) | ||
| Dm = M \ (Qm + B / 2) |
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| @@ -0,0 +1,42 @@ | ||
| using Test | ||
| using LinearAlgebra | ||
| using SummationByPartsOperators | ||
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| # check construction of interior part of upwind operators | ||
| @testset "Check interior parts" begin | ||
| N = 21 | ||
| xmin = 0//1 | ||
| xmax = (N + 1) // 1 | ||
| interior = 10:N-10 | ||
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| for acc_order in 2:4 | ||
| Dp_bounded = derivative_operator(Mattsson2017(:plus ), 1, acc_order, xmin, xmax, N) | ||
| Dm_bounded = derivative_operator(Mattsson2017(:minus ), 1, acc_order, xmin, xmax, N) | ||
| Dc_bounded = derivative_operator(Mattsson2017(:central), 1, acc_order, xmin, xmax, N) | ||
| println(devnull, Dp_bounded) | ||
| M = mass_matrix(Dp_bounded) | ||
| @test M == mass_matrix(Dm_bounded) | ||
| @test M == mass_matrix(Dc_bounded) | ||
| Dp_periodic = periodic_derivative_operator(1, acc_order, xmin, xmax, N, -(acc_order - 1) ÷ 2) | ||
| Dm_periodic = periodic_derivative_operator(1, acc_order, xmin, xmax, N, -acc_order + (acc_order - 1) ÷ 2) | ||
| Dp = Matrix(Dp_bounded) | ||
| Dm = Matrix(Dm_bounded) | ||
| @test Dp[interior,interior] ≈ Matrix(Dp_periodic)[interior,interior] | ||
| @test Dm[interior,interior] ≈ Matrix(Dm_periodic)[interior,interior] | ||
| res = M * Dp + Dm' * M | ||
| res[1,1] += 1 | ||
| res[end,end] -= 1 | ||
| @test norm(res) < 10N * eps() | ||
| x = grid(Dp_bounded) | ||
| for D in (Dp_bounded, Dm_bounded, Dc_bounded) | ||
| @test norm(D * x.^0) < 10N * eps() | ||
| for k in 1:acc_order÷2 | ||
| @test D * x.^k ≈ k .* x.^(k-1) | ||
| end | ||
| for k in acc_order÷2+1:acc_order | ||
| @test (D * x.^k)[interior] ≈ (k .* x.^(k-1))[interior] | ||
| end | ||
| end | ||
| end | ||
| end |