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Allow Fourier and periodic rational derivative operators for BBMBBMEquations1D and SvaerdKalischEquations1D #154

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Sep 24, 2024
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Allow Fourier and periodic rational derivative operators for BBMBBMEquations1D and SvaerdKalischEquations1D #154

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4c1223f
allow Fourier and periodic rational derivative operators
JoshuaLampert Sep 23, 2024
4570853
format
JoshuaLampert Sep 23, 2024
4114bbb
adjust tolerances
JoshuaLampert Sep 23, 2024
5fd46d6
avoid clutter
JoshuaLampert Sep 23, 2024
8dd383e
fix
JoshuaLampert Sep 23, 2024
950828f
add test for PeriodicRationalDerivativeOperator for BBMEquation1D
JoshuaLampert Sep 23, 2024
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2 changes: 1 addition & 1 deletion examples/bbm_1d/bbm_1d_basic.jl
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Expand Up @@ -28,7 +28,7 @@ semi = Semidiscretization(mesh, equations, initial_condition, solver,
tspan = (0.0, 1000.0)
ode = semidiscretize(semi, tspan)
summary_callback = SummaryCallback()
analysis_callback = AnalysisCallback(semi; interval = 10,
analysis_callback = AnalysisCallback(semi; interval = 100,
extra_analysis_errors = (:conservation_error,),
extra_analysis_integrals = (waterheight_total,
entropy_modified,
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2 changes: 1 addition & 1 deletion examples/bbm_1d/bbm_1d_fourier.jl
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Expand Up @@ -30,7 +30,7 @@ semi = Semidiscretization(mesh, equations, initial_condition, solver,
tspan = (0.0, 1000.0)
ode = semidiscretize(semi, tspan)
summary_callback = SummaryCallback()
analysis_callback = AnalysisCallback(semi; interval = 10,
analysis_callback = AnalysisCallback(semi; interval = 100,
extra_analysis_errors = (:conservation_error,),
extra_analysis_integrals = (waterheight_total,
entropy_modified,
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2 changes: 1 addition & 1 deletion examples/bbm_1d/bbm_1d_hamiltonian_relaxation.jl
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Expand Up @@ -28,7 +28,7 @@ semi = Semidiscretization(mesh, equations, initial_condition, solver,
tspan = (0.0, 1000.0)
ode = semidiscretize(semi, tspan)
summary_callback = SummaryCallback()
analysis_callback = AnalysisCallback(semi; interval = 10,
analysis_callback = AnalysisCallback(semi; interval = 100,
extra_analysis_errors = (:conservation_error,),
extra_analysis_integrals = (waterheight_total,
entropy_modified,
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2 changes: 1 addition & 1 deletion examples/bbm_1d/bbm_1d_relaxation.jl
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Expand Up @@ -28,7 +28,7 @@ semi = Semidiscretization(mesh, equations, initial_condition, solver,
tspan = (0.0, 1000.0)
ode = semidiscretize(semi, tspan)
summary_callback = SummaryCallback()
analysis_callback = AnalysisCallback(semi; interval = 10,
analysis_callback = AnalysisCallback(semi; interval = 100,
extra_analysis_errors = (:conservation_error,),
extra_analysis_integrals = (waterheight_total,
entropy_modified,
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43 changes: 43 additions & 0 deletions examples/bbm_bbm_1d/bbm_bbm_1d_fourier.jl
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@@ -0,0 +1,43 @@
using OrdinaryDiffEq
using DispersiveShallowWater
using SummationByPartsOperators: fourier_derivative_operator

###############################################################################
# Semidiscretization of the BBM-BBM equation

# or bathymetry_variable instead of bathymetry_flat
equations = BBMBBMEquations1D(bathymetry_type = bathymetry_flat, gravity_constant = 9.81)

# initial_condition_convergence_test needs periodic boundary conditions
initial_condition = initial_condition_convergence_test
boundary_conditions = boundary_condition_periodic

# create homogeneous mesh
coordinates_min = -35.0
coordinates_max = 35.0
N = 512
mesh = Mesh1D(coordinates_min, coordinates_max, N)

# create solver with Fourier SBP operators
D1 = fourier_derivative_operator(xmin(mesh), xmax(mesh), nnodes(mesh))
D2 = D1^2
solver = Solver(D1, D2)

# semidiscretization holds all the necessary data structures for the spatial discretization
semi = Semidiscretization(mesh, equations, initial_condition, solver,
boundary_conditions = boundary_conditions)

###############################################################################
# Create `ODEProblem` and run the simulation
tspan = (0.0, 30.0)
ode = semidiscretize(semi, tspan)
summary_callback = SummaryCallback()
analysis_callback = AnalysisCallback(semi; interval = 10,
extra_analysis_errors = (:conservation_error,),
extra_analysis_integrals = (waterheight_total,
velocity, entropy))
callbacks = CallbackSet(analysis_callback, summary_callback)

saveat = range(tspan..., length = 100)
sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7,
save_everystep = false, callback = callbacks, saveat = saveat)
43 changes: 43 additions & 0 deletions examples/svaerd_kalisch_1d/svaerd_kalisch_1d_dingemans_fourier.jl
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@@ -0,0 +1,43 @@
using OrdinaryDiffEq
using DispersiveShallowWater
using SummationByPartsOperators: fourier_derivative_operator

###############################################################################
# Semidiscretization of the Svärd-Kalisch equations

equations = SvaerdKalischEquations1D(gravity_constant = 9.81, eta0 = 0.8, alpha = 0.0,
beta = 0.27946992481203003, gamma = 0.0521077694235589)

initial_condition = initial_condition_dingemans
boundary_conditions = boundary_condition_periodic

# create homogeneous mesh
coordinates_min = -138.0
coordinates_max = 46.0
N = 512
mesh = Mesh1D(coordinates_min, coordinates_max, N)

# create solver with Fourier SBP operators
D1 = fourier_derivative_operator(xmin(mesh), xmax(mesh), nnodes(mesh))
D2 = D1^2
solver = Solver(D1, D2)

# semidiscretization holds all the necessary data structures for the spatial discretization
semi = Semidiscretization(mesh, equations, initial_condition, solver,
boundary_conditions = boundary_conditions)

###############################################################################
# Create `ODEProblem` and run the simulation
tspan = (0.0, 70.0)
ode = semidiscretize(semi, tspan)
summary_callback = SummaryCallback()
analysis_callback = AnalysisCallback(semi; interval = 10,
extra_analysis_errors = (:conservation_error,),
extra_analysis_integrals = (waterheight_total,
entropy,
entropy_modified))
callbacks = CallbackSet(analysis_callback, summary_callback)

saveat = range(tspan..., length = 500)
sol = solve(ode, Tsit5(), abstol = 1e-7, reltol = 1e-7,
save_everystep = false, callback = callbacks, saveat = saveat)
2 changes: 1 addition & 1 deletion src/equations/bbm_1d.jl
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Expand Up @@ -176,7 +176,7 @@
@.. deta = -(0.75 * c_1 * eta2_x + c_0 * eta_x_upwind)
end
else
@error "unknown type of first-derivative operator: $(typeof(solver.D1))"
throw(ArgumentError("unknown type of first-derivative operator: $(typeof(solver.D1))"))

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end
end

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25 changes: 15 additions & 10 deletions src/equations/bbm_bbm_1d.jl
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Expand Up @@ -299,13 +299,14 @@
end
K = Diagonal(D .^ 2)
if solver.D1 isa PeriodicDerivativeOperator ||
solver.D1 isa UniformPeriodicCoupledOperator
solver.D1 isa UniformPeriodicCoupledOperator ||
solver.D1 isa FourierDerivativeOperator
sparse_D1 = sparse(solver.D1)
invImDKD = lu(I - 1 / 6 * sparse_D1 * K * sparse_D1)
elseif solver.D1 isa PeriodicUpwindOperators
invImDKD = lu(I - 1 / 6 * sparse(solver.D1.minus) * K * sparse(solver.D1.plus))
else
@error "unknown type of first-derivative operator: $(typeof(solver.D1))"
throw(ArgumentError("unknown type of first-derivative operator: $(typeof(solver.D1))"))

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end
invImD2K = lu(I - 1 / 6 * sparse(solver.D2) * K)

Expand Down Expand Up @@ -337,14 +338,15 @@

# homogeneous Neumann boundary conditions
if solver.D1 isa DerivativeOperator ||
solver.D1 isa UniformCoupledOperator
solver.D1 isa UniformCoupledOperator ||
solver.D1 isa FourierDerivativeOperator
D1_b = BandedMatrix(solver.D1)
invImD2n = lu(I + 1 / 6 * D^2 * inv(M) * D1_b' * PdM * D1_b)
elseif solver.D1 isa UpwindOperators
D1plus_b = BandedMatrix(solver.D1.plus)
invImD2n = lu(I + 1 / 6 * D^2 * inv(M) * D1plus_b' * PdM * D1plus_b)
else
@error "unknown type of first-derivative operator: $(typeof(solver.D1))"
throw(ArgumentError("unknown type of first-derivative operator: $(typeof(solver.D1))"))

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end

# create temporary storage
Expand Down Expand Up @@ -380,14 +382,15 @@

# homogeneous Neumann boundary conditions
if solver.D1 isa DerivativeOperator ||
solver.D1 isa UniformCoupledOperator
solver.D1 isa UniformCoupledOperator ||
solver.D1 isa FourierDerivativeOperator
D1_b = BandedMatrix(solver.D1)
invImD2n = lu(I + 1 / 6 * inv(M) * D1_b' * PdM * K * D1_b)
elseif solver.D1 isa UpwindOperators
D1plus_b = BandedMatrix(solver.D1.plus)
invImD2n = lu(I + 1 / 6 * inv(M) * D1plus_b' * PdM * K * D1plus_b)
else
@error "unknown type of first-derivative operator: $(typeof(solver.D1))"
throw(ArgumentError("unknown type of first-derivative operator: $(typeof(solver.D1))"))

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end

# create temporary storage
Expand Down Expand Up @@ -431,7 +434,8 @@
end
# energy and mass conservative semidiscretization
if solver.D1 isa PeriodicDerivativeOperator ||
solver.D1 isa UniformPeriodicCoupledOperator
solver.D1 isa UniformPeriodicCoupledOperator ||
solver.D1 isa FourierDerivativeOperator
@trixi_timeit timer() "deta hyperbolic" begin
mul!(deta, solver.D1, tmp1)
end
Expand All @@ -446,7 +450,7 @@
mul!(dv, solver.D1.plus, tmp2)
end
else
@error "unknown type of first-derivative operator: $(typeof(solver.D1))"
throw(ArgumentError("unknown type of first-derivative operator: $(typeof(solver.D1))"))

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end

@trixi_timeit timer() "source terms" calc_sources!(dq, q, t, source_terms, equations,
Expand Down Expand Up @@ -497,7 +501,8 @@
end
# energy and mass conservative semidiscretization
if solver.D1 isa DerivativeOperator ||
solver.D1 isa UniformCoupledOperator
solver.D1 isa UniformCoupledOperator ||
solver.D1 isa FourierDerivativeOperator
@trixi_timeit timer() "deta hyperbolic" begin
mul!(deta, solver.D1, tmp1)
end
Expand All @@ -512,7 +517,7 @@
mul!(dv, solver.D1.plus, tmp2)
end
else
@error "unknown type of first-derivative operator: $(typeof(solver.D1))"
throw(ArgumentError("unknown type of first-derivative operator: $(typeof(solver.D1))"))

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end

@trixi_timeit timer() "source terms" calc_sources!(dq, q, t, source_terms, equations,
Expand Down
10 changes: 6 additions & 4 deletions src/equations/svaerd_kalisch_1d.jl
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Expand Up @@ -178,7 +178,8 @@
M_beta = copy(beta_hat)
scale_by_mass_matrix!(M_beta, D1)
if D1 isa PeriodicDerivativeOperator ||
D1 isa UniformPeriodicCoupledOperator
D1 isa UniformPeriodicCoupledOperator ||
D1 isa FourierDerivativeOperator
D1_central = D1
D1mat = sparse(D1_central)
minus_MD1betaD1 = D1mat' * Diagonal(M_beta) * D1mat
Expand All @@ -195,7 +196,7 @@
D1, D1mat_minus, equations)
end
else
@error "unknown type of first-derivative operator: $(typeof(D1))"
throw(ArgumentError("unknown type of first-derivative operator: $(typeof(D1))"))

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end
factorization = cholesky(system_matrix)
cache = (; factorization, minus_MD1betaD1, D, h, hv, b, eta_x, v_x,
Expand Down Expand Up @@ -251,7 +252,8 @@
@.. hv = h * v

if D1 isa PeriodicDerivativeOperator ||
D1 isa UniformPeriodicCoupledOperator
D1 isa UniformPeriodicCoupledOperator ||
D1 isa FourierDerivativeOperator
mul!(eta_x, D1_central, eta)
mul!(v_x, D1_central, v)
@.. tmp1 = alpha_hat * eta_x
Expand Down Expand Up @@ -282,7 +284,7 @@
mul!(deta, D1.minus, tmp1)
mul!(deta, D1_central, hv, -1.0, 1.0)
else
@error "unknown type of first derivative operator: $(typeof(D1))"
throw(ArgumentError("unknown type of first-derivative operator: $(typeof(D1))"))

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end
end

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3 changes: 2 additions & 1 deletion src/solver.jl
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Expand Up @@ -26,7 +26,8 @@ struct Solver{RealT <: Real,
}
@assert derivative_order(D1) == 1
if D2 isa AbstractDerivativeOperator &&
!(D2 isa SummationByPartsOperators.FourierPolynomialDerivativeOperator)
!(D2 isa SummationByPartsOperators.FourierPolynomialDerivativeOperator) &&
!(D2 isa SummationByPartsOperators.PeriodicRationalDerivativeOperator)
@assert derivative_order(D2) == 2
end
new(D1, D2)
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17 changes: 17 additions & 0 deletions test/test_bbm_1d.jl
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Expand Up @@ -41,6 +41,23 @@ end
end

@test_allocations(semi, sol, allocs=5_000)

# test PeriodicRationalDerivativeOperator
D1 = periodic_derivative_operator(1, accuracy_order, xmin(mesh), xmax(mesh),
nnodes(mesh))
D2 = D1^2
solver = Solver(D1, D2)
Comment on lines +45 to +49
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If we go as far as this, it could make sense to add downstream tests to SummationByPartsOperators.jl. I am not sure whether I have documented that D1^ will necessarily return a PeriodicRationalDerivativeOperator. It should be pretty stable, but we use some parts that are less clearly described as public API.

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Ok, I didn't know that PeriodicRationalDerivativeOperator is not quite public. Adding tests to SummationByPartsOperators.jl sounds good. But this can be merged anyway, right?

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The same also holds for FourierPolynomialDerivativeOperator, doesn't it? As far as I can tell, it's also not clearly documented that D1^ will return a FourierPolynomialDerivativeOperator if D1 is a FourierDerivativeOperator.

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Well, I have not added any documentation to it, so it is indeed not really public but more like an implementation detail to make ^ etc. work - which is documented

All of these periodic derivative operators support multiplication and addition such that polynomials and rational functions of them can be represented efficiently

already in the README.md (see https://github.com/ranocha/SummationByPartsOperators.jl?tab=readme-ov-file#periodic-domains).

But we can go ahead and merge this PR here. We don't need to add downstream tests right now, but it may be nice to keep this in mind for the future.

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The simpler option would be to add some explicit tests that ^ returns the appropriate types with some comments that DispersiveShallowWater.jl uses this interface.

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The same also holds for FourierPolynomialDerivativeOperator, doesn't it? As far as I can tell, it's also not clearly documented that D1^ will return a FourierPolynomialDerivativeOperator if D1 is a FourierDerivativeOperator.

Yes

@test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_1d_basic.jl"),
tspan=(0.0, 100.0),
solver=solver,
l2=[0.013447144236536044],
linf=[0.007184057857459125],
cons_error=[1.5543122344752192e-15],
change_waterheight=-1.5543122344752192e-15,
change_entropy_modified=-8.68871272874383e-7,
change_hamiltonian=-3.697687313897191e-6)

@test_allocations(semi, sol, allocs=5_000)
end

@testitem "bbm_1d_basic with split_form = false" setup=[
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47 changes: 47 additions & 0 deletions test/test_bbm_bbm_1d.jl
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Expand Up @@ -42,6 +42,24 @@ end
end

@test_allocations(semi, sol, allocs=10_000)

# test PeriodicRationalDerivativeOperator
D1 = periodic_derivative_operator(1, accuracy_order, xmin(mesh), xmax(mesh),
nnodes(mesh))
D2 = D1^2
solver = Solver(D1, D2)
@test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_bbm_1d_basic.jl"),
tspan=(0.0, 1.0),
solver=solver,
l2=[0.0016951648276611925 0.0034269307395771303 0.0],
linf=[0.001453478820216958 0.001805665634286413 0.0],
cons_error=[2.055466838899258e-14 0.0 0.0],
change_waterheight=2.055466838899258e-14,
change_velocity=0.0,
change_entropy=0.00023833941781958856,
atol_ints=1e-10) # to make CI pass

@test_allocations(semi, sol, allocs=10_000)
end

@testitem "bbm_bbm_1d_basic with bathymetry_variable" setup=[Setup, BBMBBMEquation1D] begin
Expand Down Expand Up @@ -86,6 +104,35 @@ end
@test_allocations(semi, sol, allocs=10_000)
end

@testitem "bbm_bbm_1d_fourier" setup=[Setup, BBMBBMEquation1D] begin
@test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_bbm_1d_fourier.jl"),
tspan=(0.0, 1.0),
l2=[7.291521968885259e-7 7.702204594455217e-7 0.0],
linf=[4.3579646391567195e-7 4.9442969896063e-7 0.0],
cons_error=[3.9206314028412105e-14 4.547473508864641e-13 0.0],
change_waterheight=3.9206314028412105e-14,
change_velocity=-4.547473508864641e-13,
change_entropy=0.0002383147650562023,
atol_ints=1e-10) # to make CI pass

@test_allocations(semi, sol, allocs=10_000)
end

@testitem "bbm_bbm_1d_fourier with bathymetry_variable" setup=[Setup, BBMBBMEquation1D] begin
@test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_bbm_1d_fourier.jl"),
bathymetry_type=bathymetry_variable,
tspan=(0.0, 1.0),
l2=[7.291481123937497e-7 7.70214005540768e-7 0.0],
linf=[4.357912374297612e-7 4.94414834406598e-7 0.0],
cons_error=[6.232593470137382e-13 4.547473508864641e-13 0.0],
change_waterheight=6.232593470137382e-13,
change_velocity=-4.547473508864641e-13,
change_entropy=0.0002383154298968293,
atol_ints=1e-10) # to make CI pass

@test_allocations(semi, sol, allocs=10_000)
end

@testitem "bbm_bbm_1d_relaxation" setup=[Setup, BBMBBMEquation1D] begin
@test_trixi_include(joinpath(EXAMPLES_DIR, "bbm_bbm_1d_relaxation.jl"),
tspan=(0.0, 1.0),
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