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b/docs/Project.toml @@ -2,6 +2,7 @@ CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" DocumenterCitations = "daee34ce-89f3-4625-b898-19384cb65244" +Implicit = "7f538e44-2768-4ef2-af90-2110c0378286" KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c" Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7" KrylovPreconditioners = "45d422c2-293f-44ce-8315-2cb988662dec" @@ -9,9 +10,13 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" Literate = "98b081ad-f1c9-55d3-8b20-4c87d4299306" Ariadne = "0be81120-40bf-4f8b-adf0-26103efb66f1" OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881" +OrdinaryDiffEqLowStorageRK = "b0944070-b475-4768-8dec-fb6eb410534d" +OrdinaryDiffEqSSPRK = "669c94d9-1f4b-4b64-b377-1aa079aa2388" PlutoStaticHTML = "359b1769-a58e-495b-9770-312e911026ad" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" SummationByPartsOperators = "9f78cca6-572e-554e-b819-917d2f1cf240" +Trixi = "a7f1ee26-1774-49b1-8366-f1abc58fbfcb" [sources] Ariadne = {path = ".."} +Implicit = {path = "../libs/Implicit"} diff --git a/docs/make.jl b/docs/make.jl index 330e9de..75f1657 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -49,6 +49,7 @@ examples = [ "Implicit -- Heat 1D" => "heat_1D", "Implicit -- Heat 1D DG" => "heat_1D_DG", "Implicit -- Heat 2D" => "heat_2D", + "Trixi" => "trixi", ] for (_, name) in examples diff --git a/docs/src/refs.bib b/docs/src/refs.bib index 1605a8a..5abda41 100644 --- a/docs/src/refs.bib +++ b/docs/src/refs.bib @@ -51,3 +51,50 @@ @ARTICLE{Kan2022-ko urldate = {2024-10-21}, language = {en} } + +@ARTICLE{Hosea1996-xv, + title = {Analysis and implementation of {TR}-{BDF2}}, + author = {Hosea, M E and Shampine, L F}, + journaltitle = {Applied numerical mathematics: transactions of IMACS}, + publisher = {Elsevier BV}, + volume = {20}, + issue = {1-2}, + pages = {21--37}, + date = {1996-02-01}, + doi = {10.1016/0168-9274(95)00115-8}, + issn = {0168-9274,1873-5460}, + urldate = {2025-03-04}, + language = {en} +} + +@ARTICLE{Bank1985-gh, + title = {Transient simulation of silicon devices and circuits}, + author = {Bank, R E and Coughran, W M and Fichtner, W and Grosse, E H + and Rose, D J and Smith, R K}, + journaltitle = {IEEE transactions on electron devices}, + publisher = {Institute of Electrical and Electronics Engineers (IEEE)}, + volume = {32}, + issue = {10}, + pages = {1992--2007}, + date = {1985-10}, + doi = {10.1109/t-ed.1985.22232}, + issn = {0018-9383,1557-9646}, + urldate = {2025-05-27}, + language = {en} +} + +@ARTICLE{Bonaventura2021-za, + title = {The {TR}-{BDF2} method for second order problems in structural + mechanics}, + author = {Bonaventura, Luca and Mármol, Macarena Gómez}, + journaltitle = {Computers \& mathematics with applications (Oxford, England: + 1987)}, + publisher = {Elsevier BV}, + volume = {92}, + pages = {13--26}, + date = {2021-06-15}, + doi = {10.1016/j.camwa.2021.03.037}, + issn = {0898-1221,1873-7668}, + urldate = {2025-05-27}, + language = {en} +} diff --git a/examples/LocalPreferences.toml b/examples/LocalPreferences.toml new file mode 100644 index 0000000..11d9f7e --- /dev/null +++ b/examples/LocalPreferences.toml @@ -0,0 +1,3 @@ +[Trixi] +loop_vectorization = false +polyester = false diff --git a/examples/Manifest.toml b/examples/Manifest.toml new file mode 100644 index 0000000..f9db8fc --- /dev/null +++ b/examples/Manifest.toml @@ -0,0 +1,3114 @@ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.11.5" +manifest_format = "2.0" +project_hash = "bd968805694a58fc0357e8b0ea61144c0696459a" + +[[deps.ADTypes]] +git-tree-sha1 = "be7ae030256b8ef14a441726c4c37766b90b93a3" +uuid = "47edcb42-4c32-4615-8424-f2b9edc5f35b" +version = "1.15.0" +weakdeps = ["ChainRulesCore", "ConstructionBase", "EnzymeCore"] + + [deps.ADTypes.extensions] + ADTypesChainRulesCoreExt = "ChainRulesCore" + ADTypesConstructionBaseExt = 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+[[deps.libwebp_jll]] +deps = ["Artifacts", "Giflib_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libglvnd_jll", "Libtiff_jll", "libpng_jll"] +git-tree-sha1 = "4e4282c4d846e11dce56d74fa8040130b7a95cb3" +uuid = "c5f90fcd-3b7e-5836-afba-fc50a0988cb2" +version = "1.6.0+0" + +[[deps.nghttp2_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" +version = "1.59.0+0" + +[[deps.oneTBB_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "d5a767a3bb77135a99e433afe0eb14cd7f6914c3" +uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e" +version = "2022.0.0+0" + +[[deps.p7zip_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" +version = "17.4.0+2" + +[[deps.t8code_jll]] +deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl", "MPICH_jll", "MPIPreferences", "MPItrampoline_jll", "MicrosoftMPI_jll", "OpenMPI_jll", "TOML", "Zlib_jll"] +git-tree-sha1 = "cf073e7d4275b8a030140936639f3d6a5eeb3e74" +uuid = "4ee9bed8-4011-53f7-90c2-22363c2f500d" +version = "3.0.1+0" + +[[deps.x264_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2" +uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" +version = "2021.5.5+0" + +[[deps.x265_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" +uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" +version = "3.5.0+0" diff --git a/examples/Project.toml b/examples/Project.toml index 675a3da..a010312 100644 --- a/examples/Project.toml +++ b/examples/Project.toml @@ -1,16 +1,27 @@ [deps] +Ariadne = "0be81120-40bf-4f8b-adf0-26103efb66f1" CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" -ComponentArrays = "b0b7db55-cfe3-40fc-9ded-d10e2dbeff66" +DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63" Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9" +Implicit = "7f538e44-2768-4ef2-af90-2110c0378286" KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c" Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7" KrylovPreconditioners = "45d422c2-293f-44ce-8315-2cb988662dec" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" -Ariadne = "0be81120-40bf-4f8b-adf0-26103efb66f1" Observables = "510215fc-4207-5dde-b226-833fc4488ee2" OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881" +OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" +OrdinaryDiffEqLowStorageRK = "b0944070-b475-4768-8dec-fb6eb410534d" +OrdinaryDiffEqSDIRK = "2d112036-d095-4a1e-ab9a-08536f3ecdbf" +OrdinaryDiffEqSSPRK = "669c94d9-1f4b-4b64-b377-1aa079aa2388" +Revise = "295af30f-e4ad-537b-8983-00126c2a3abe" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" SummationByPartsOperators = "9f78cca6-572e-554e-b819-917d2f1cf240" +Trixi = "a7f1ee26-1774-49b1-8366-f1abc58fbfcb" [sources] Ariadne = {path = ".."} +Implicit = {path = "../libs/Implicit"} + +[compat] +julia = "1.10" diff --git a/examples/implicit.jl b/examples/implicit.jl index c0e84a1..46cbdae 100644 --- a/examples/implicit.jl +++ b/examples/implicit.jl @@ -1,8 +1,6 @@ # # [Implicit schemes](@id implicit_schemes) using Ariadne -using Ariadne - # ## Implicit Euler function G_Euler!(res, uₙ, Δt, f!, du, u, p, t) diff --git a/examples/trixi.jl b/examples/trixi.jl new file mode 100644 index 0000000..3e1f79e --- /dev/null +++ b/examples/trixi.jl @@ -0,0 +1,140 @@ +# # Using the an implicit solver based on Ariadne with Trixi.jl + +using Trixi +using Implicit +using CairoMakie + + +# Notes: +# Must disable both Polyester and LoopVectorization for Enzyme to be able to differentiate Trixi.jl +# Using https://github.com/trixi-framework/Trixi.jl/pull/2295 +# +# LocalPreferences.jl +# ```toml +# [Trixi] +# loop_vectorization = false +# polyester = false +# ``` + +@assert !Trixi._PREFERENCE_POLYESTER +@assert !Trixi._PREFERENCE_LOOPVECTORIZATION + +# ## Load Trixi Example +# trixi_include(joinpath(examples_dir(), "tree_2d_dgsem", "elixir_advection_basic.jl"), sol = nothing); +trixi_include(joinpath(examples_dir(), "tree_2d_dgsem", "elixir_advection_basic.jl")); + +ref = copy(sol) + +u = copy(ode.u0) +du = zero(ode.u0) +res = zero(ode.u0) + +F! = Implicit.nonlinear_problem(Implicit.ImplicitEuler(), ode.f) +J = Implicit.Ariadne.JacobianOperator(F!, res, u, (ode.u0, 1.0, du, ode.p, 0.0, (), 1)) + +collect(J) + +using LinearAlgebra +out = zero(u) +v = zero(u) +@time mul!(u, J, v) +@time F!(res, u, (ode.u0, 1.0, du, ode.p, 0.0, (), 1)) + +F! = Implicit.nonlinear_problem(Implicit.SDIRK2(), ode.f) +u1 = copy(ode.u0) +u2 = copy(u1) +J1 = Implicit.Ariadne.JacobianOperator(F!, res, u1, (ode.u0, 1.0, du, ode.p, 0.0, (u1,), 1)) +J2 = Implicit.Ariadne.JacobianOperator(F!, res, u2, (ode.u0, 1.0, du, ode.p, 0.0, (u1,), 2)) + +using LinearAlgebra +out = zero(u) +v = zero(u) +@time F!(res, u, (ode.u0, 1.0, du, ode.p, 0.0, (u1,), 1)) +@time mul!(u, J1, v) + +collect(J1) +collect(J2) + +# Cost of time(Jvp) ≈ 2 * time(rhs) + +# ### Jacobian (of the implicit function given the ode) +J = Implicit.jacobian(Implicit.ImplicitEuler(), ode, 1.0) + +# ### Solve using ODE interface + +sol = solve( + ode, Implicit.ImplicitEuler(); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, + # krylov_kwargs=(;verbose=1) +); + +sol = solve( + ode, Implicit.ImplicitMidpoint(); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, + # krylov_kwargs=(;verbose=1) +); + +sol = solve( + ode, Implicit.ImplicitTrapezoid(); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, + # krylov_kwargs=(;verbose=1) +); + + +sol = solve( + ode, Implicit.TRBDF2(); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, + # krylov_kwargs=(;verbose=1) +); + +import OrdinaryDiffEqSDIRK +import DifferentiationInterface: AutoFiniteDiff +sol = solve( + ode, OrdinaryDiffEqSDIRK.TRBDF2(autodiff = AutoFiniteDiff()); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + adaptive = false +); + +# ### Plot the (reference) solution + +# We have to manually convert the sol since Implicit has it's own leightweight solution type. +# Create an extension. +## pd = PlotData2D(sol.u[end], sol.prob.p) + +plot(Trixi.PlotData2DTriangulated(ref.u[1], ref.prob.p)) + +# ### Plot the solution + +plot(Trixi.PlotData2DTriangulated(sol.u[end], sol.prob.p)) + +# ## Increase CFL numbers + +trixi_include(joinpath(examples_dir(), "tree_2d_dgsem", "elixir_advection_basic.jl"), cfl = 10, sol = nothing); + +sol = solve( + ode, Implicit.ImplicitEuler(); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, + # krylov_kwargs=(;verbose=1) +); + +@show callbacks.discrete_callbacks[4] + +# ### Plot the solution + +plot(Trixi.PlotData2DTriangulated(sol.u[end], sol.prob.p)) diff --git a/examples/trixi_adv_diff_imex.jl b/examples/trixi_adv_diff_imex.jl new file mode 100644 index 0000000..1fa5e95 --- /dev/null +++ b/examples/trixi_adv_diff_imex.jl @@ -0,0 +1,103 @@ +# # Using the an implicit solver based on Ariadne with Trixi.jl + +using Trixi +using Implicit +using CairoMakie +using OrdinaryDiffEqLowStorageRK +# Notes: +# Must disable both Polyester and LoopVectorization for Enzyme to be able to differentiate Trixi.jl +# Using https://github.com/trixi-framework/Trixi.jl/pull/2295 +# +# LocalPreferences.jl +# ```toml +# [Trixi] +# loop_vectorization = false +# polyester = false +# ``` + +@assert !Trixi._PREFERENCE_POLYESTER +@assert !Trixi._PREFERENCE_LOOPVECTORIZATION + + +############################################################################### +# semidiscretization of the linear advection-diffusion equation + +advection_velocity = (1.5, 1.0) +equations = LinearScalarAdvectionEquation2D(advection_velocity) +diffusivity() = 1.0 +equations_parabolic = LaplaceDiffusion2D(diffusivity(), equations) + +# Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) + +coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) + +# Create a uniformly refined mesh with periodic boundaries +mesh = TreeMesh(coordinates_min, coordinates_max, + initial_refinement_level = 4, + periodicity = true, + n_cells_max = 30_000) # set maximum capacity of tree data structure + +# Define initial condition +function initial_condition_diffusive_convergence_test(x, t, + equation::LinearScalarAdvectionEquation2D) + # Store translated coordinate for easy use of exact solution + RealT = eltype(x) + x_trans = x - equation.advection_velocity * t + + nu = diffusivity() + c = 1 + A = 0.5f0 + L = 2 + f = 1.0f0 / L + omega = 2 * convert(RealT, pi) * f + scalar = c + A * sin(omega * sum(x_trans)) * exp(-2 * nu * omega^2 * t) + return SVector(scalar) +end +initial_condition = initial_condition_diffusive_convergence_test + +# define periodic boundary conditions everywhere +boundary_conditions = boundary_condition_periodic +boundary_conditions_parabolic = boundary_condition_periodic + +# A semidiscretization collects data structures and functions for the spatial discretization +semi = SemidiscretizationHyperbolicParabolic(mesh, + (equations, equations_parabolic), + initial_condition, solver; + solver_parabolic = ViscousFormulationBassiRebay1(), + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic)) + +############################################################################### +# ODE solvers, callbacks etc. + +# Create ODE problem with time span from 0.0 to 1.5 +tspan = (0.0, 1.5) +ode = semidiscretize(semi, tspan) + +# At the beginning of the main loop, the SummaryCallback prints a summary of the simulation setup +# and resets the timers +summary_callback = SummaryCallback() + +# The AnalysisCallback allows to analyse the solution in regular intervals and prints the results +analysis_interval = 100 +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) + +# The AliveCallback prints short status information in regular intervals +alive_callback = AliveCallback(analysis_interval = analysis_interval) + +# Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver +callbacks = CallbackSet(summary_callback, analysis_callback, alive_callback) + +############################################################################### +# run the simulation + +sol = solve( + ode, + Implicit.RKImplicitExplicitEuler(); + dt = 0.001, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, +); diff --git a/examples/trixi_convergence.jl b/examples/trixi_convergence.jl new file mode 100644 index 0000000..d097e1c --- /dev/null +++ b/examples/trixi_convergence.jl @@ -0,0 +1,56 @@ +# # Using the an implicit solver based on Ariadne with Trixi.jl + +using Trixi +using Implicit +using CairoMakie + + +# Notes: +# Must disable both Polyester and LoopVectorization for Enzyme to be able to differentiate Trixi.jl +# Using https://github.com/trixi-framework/Trixi.jl/pull/2295 +# +# LocalPreferences.jl +# ```toml +# [Trixi] +# loop_vectorization = false +# polyester = false +# ``` + +@assert !Trixi._PREFERENCE_POLYESTER +@assert !Trixi._PREFERENCE_LOOPVECTORIZATION + +trixi_include(joinpath(examples_dir(), "tree_2d_dgsem", "elixir_advection_basic.jl"), cfl = 1.25/2, sol = nothing, save_solution = nothing, + initial_refinement_level = 6, advection_velocity = (1.0, 1.0)); + +ode = semidiscretize(semi, (0.0, 2.0)) + +############################################################################### +# run the simulation + +sol = solve( + ode, + # Implicit.RKImplicitEuler(); + # Implicit.KS22(); + # Implicit.C23(); + # Implicit.L33(); + Implicit.RKTRBDF2(); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, +); + +cfl_vec = [10.0, 5.0, 2.5, 1.25, 1.25/2] +l2_vec = [1.07287321e-02, 2.69376612e-03, 6.75387935e-04, 1.68974528e-04, 4.22696680e-05] +linf_vec = [1.51727157e-02, 3.80957386e-03, 9.55254494e-04, 2.38966657e-04, 5.97799432e-05] +f = Figure() +ax = Axis(f[1, 1], xlabel = "CFL", ylabel = "Error", + xscale = log10, yscale = log10, title = "Convergence Plot") + +lines!(ax, cfl_vec, l2_vec, label = "L2 norm") +lines!(ax, cfl_vec, linf_vec, label = "L∞ norm") +lines!(ax, cfl_vec, 1e-4.*cfl_vec.^2, label = "2nd order") + +axislegend(ax; position = :rb) + +f \ No newline at end of file diff --git a/examples/trixi_dirk.jl b/examples/trixi_dirk.jl new file mode 100644 index 0000000..4f5d358 --- /dev/null +++ b/examples/trixi_dirk.jl @@ -0,0 +1,38 @@ +# # Using the an implicit solver based on Ariadne with Trixi.jl + +using Trixi +using Implicit +using CairoMakie + + +# Notes: +# Must disable both Polyester and LoopVectorization for Enzyme to be able to differentiate Trixi.jl +# Using https://github.com/trixi-framework/Trixi.jl/pull/2295 +# +# LocalPreferences.jl +# ```toml +# [Trixi] +# loop_vectorization = false +# polyester = false +# ``` + +@assert !Trixi._PREFERENCE_POLYESTER +@assert !Trixi._PREFERENCE_LOOPVECTORIZATION + +trixi_include(joinpath(examples_dir(), "tree_2d_dgsem", "elixir_advection_basic.jl"), cfl = 10.0, sol = nothing, save_solution = nothing); + +############################################################################### +# run the simulation + +sol = solve( + ode, + # Implicit.RKImplicitEuler(); + # Implicit.KS22(); + # Implicit.C23(); + # Implicit.L33(); + Implicit.RKTRBDF2(); + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, +); \ No newline at end of file diff --git a/examples/trixi_fvm_lid_driven.jl b/examples/trixi_fvm_lid_driven.jl new file mode 100644 index 0000000..2f9ba74 --- /dev/null +++ b/examples/trixi_fvm_lid_driven.jl @@ -0,0 +1,83 @@ +using OrdinaryDiffEqLowStorageRK +using Trixi +using Implicit +############################################################################### +# semidiscretization of the ideal compressible Navier-Stokes equations + +prandtl_number() = 0.72 +mu = 0.001 + +equations = CompressibleEulerEquations2D(1.4) +equations_parabolic = CompressibleNavierStokesDiffusion2D(equations, mu = mu, + Prandtl = prandtl_number()) + +# Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux +solver = DGSEM(polydeg = 0, surface_flux = flux_lax_friedrichs) + +coordinates_min = (-1.0, -1.0) # minimum coordinates (min(x), min(y)) +coordinates_max = (1.0, 1.0) # maximum coordinates (max(x), max(y)) + +# Create a uniformly refined mesh +trees_per_dimension = (16, 16) +mesh = P4estMesh(trees_per_dimension, + polydeg = 0, initial_refinement_level = 0, + coordinates_min = coordinates_min, coordinates_max = coordinates_max, + periodicity = (false, false)) + +function initial_condition_cavity(x, t, equations::CompressibleEulerEquations2D) + Ma = 0.1 + rho = 1.0 + u, v = 0.0, 0.0 + p = 1.0 / (Ma^2 * equations.gamma) + return prim2cons(SVector(rho, u, v, p), equations) +end +initial_condition = initial_condition_cavity + +# BC types +velocity_bc_lid = NoSlip((x, t, equations_parabolic) -> SVector(1.0, 0.0)) +velocity_bc_cavity = NoSlip((x, t, equations_parabolic) -> SVector(0.0, 0.0)) +heat_bc = Adiabatic((x, t, equations_parabolic) -> 0.0) +boundary_condition_lid = BoundaryConditionNavierStokesWall(velocity_bc_lid, heat_bc) +boundary_condition_cavity = BoundaryConditionNavierStokesWall(velocity_bc_cavity, heat_bc) + +boundary_conditions = Dict(:x_neg => boundary_condition_slip_wall, + :y_neg => boundary_condition_slip_wall, + :y_pos => boundary_condition_slip_wall, + :x_pos => boundary_condition_slip_wall) + +boundary_conditions_parabolic = Dict(:x_neg => boundary_condition_cavity, + :y_neg => boundary_condition_cavity, + :y_pos => boundary_condition_lid, + :x_pos => boundary_condition_cavity) + +# A semidiscretization collects data structures and functions for the spatial discretization +semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic), + initial_condition, solver; + boundary_conditions = (boundary_conditions, + boundary_conditions_parabolic)) + +############################################################################### +# ODE solvers, callbacks etc. + +# Create ODE problem with time span `tspan` +tspan = (0.0, 25.0) +ode = semidiscretize(semi, tspan) + +summary_callback = SummaryCallback() +alive_callback = AliveCallback(alive_interval = 100) +analysis_interval = 100 +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) +callbacks = CallbackSet(summary_callback, alive_callback) + +############################################################################### +# run the simulation + +sol = solve( + ode, + Implicit.RKLinearImplicitExplicitEuler(); + #Implicit.KS22(); + dt = 0.00001, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, +); diff --git a/examples/trixi_imex.jl b/examples/trixi_imex.jl new file mode 100644 index 0000000..f39e5f1 --- /dev/null +++ b/examples/trixi_imex.jl @@ -0,0 +1,34 @@ +# # Using the an implicit solver based on Ariadne with Trixi.jl + +using Trixi +using Implicit +using CairoMakie + + +# Notes: +# Must disable both Polyester and LoopVectorization for Enzyme to be able to differentiate Trixi.jl +# Using https://github.com/trixi-framework/Trixi.jl/pull/2295 +# +# LocalPreferences.jl +# ```toml +# [Trixi] +# loop_vectorization = false +# polyester = false +# ``` + +@assert !Trixi._PREFERENCE_POLYESTER +@assert !Trixi._PREFERENCE_LOOPVECTORIZATION + +trixi_include(joinpath(examples_dir(), "tree_2d_dgsem", "elixir_advection_diffusion.jl"), sol = nothing); + +############################################################################### +# run the simulation + +sol = solve( + ode, + Implicit.RKImplicitExplicitEuler(); + dt = 0.001, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, +); diff --git a/examples/trixi_lid_driven_linear.jl b/examples/trixi_lid_driven_linear.jl new file mode 100644 index 0000000..5327b5c --- /dev/null +++ b/examples/trixi_lid_driven_linear.jl @@ -0,0 +1,40 @@ +# # Using the an implicit solver based on Ariadne with Trixi.jl + +using Trixi +using Implicit +using CairoMakie + + +# Notes: +# Must disable both Polyester and LoopVectorization for Enzyme to be able to differentiate Trixi.jl +# Using https://github.com/trixi-framework/Trixi.jl/pull/2295 +# +# LocalPreferences.jl +# ```toml +# [Trixi] +# loop_vectorization = false +# polyester = false +# ``` + +@assert !Trixi._PREFERENCE_POLYESTER +@assert !Trixi._PREFERENCE_LOOPVECTORIZATION + +trixi_include(joinpath(examples_dir(), "tree_2d_dgsem", "elixir_navierstokes_lid_driven_cavity.jl"), sol = nothing, mu = 0.1); + +ode = semidiscretize(semi, (0.0, 10.0)) + +############################################################################### +# run the simulation + +sol = solve( + ode, + Implicit.RKLSSPIMEX332(); + #Implicit.KS22(); + dt = 0.001, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, +); + +## dt_vec = [0.001, 0.001/2, 0.0001] +## l2_vec = [4.95311953e-04, 2.48996489e-04 ,5.40458032e-05, ] diff --git a/examples/trixi_linear_imex.jl b/examples/trixi_linear_imex.jl new file mode 100644 index 0000000..9816efc --- /dev/null +++ b/examples/trixi_linear_imex.jl @@ -0,0 +1,34 @@ +# # Using the an implicit solver based on Ariadne with Trixi.jl + +using Trixi +using Implicit +using CairoMakie + + +# Notes: +# Must disable both Polyester and LoopVectorization for Enzyme to be able to differentiate Trixi.jl +# Using https://github.com/trixi-framework/Trixi.jl/pull/2295 +# +# LocalPreferences.jl +# ```toml +# [Trixi] +# loop_vectorization = false +# polyester = false +# ``` + +@assert !Trixi._PREFERENCE_POLYESTER +@assert !Trixi._PREFERENCE_LOOPVECTORIZATION + +trixi_include(joinpath(examples_dir(), "tree_2d_dgsem", "elixir_advection_diffusion.jl"), sol = nothing); + +############################################################################### +# run the simulation + +sol = solve( + ode, + Implicit.RKLinearImplicitExplicitEuler(); + dt = 0.001, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, +); diff --git a/examples/trixi_navier_stokes_imex.jl b/examples/trixi_navier_stokes_imex.jl new file mode 100644 index 0000000..f1c641b --- /dev/null +++ b/examples/trixi_navier_stokes_imex.jl @@ -0,0 +1,38 @@ +# # Using the an implicit solver based on Ariadne with Trixi.jl + +using Trixi +using Implicit +using CairoMakie + + +# Notes: +# Must disable both Polyester and LoopVectorization for Enzyme to be able to differentiate Trixi.jl +# Using https://github.com/trixi-framework/Trixi.jl/pull/2295 +# +# LocalPreferences.jl +# ```toml +# [Trixi] +# loop_vectorization = false +# polyester = false +# ``` + +@assert !Trixi._PREFERENCE_POLYESTER +@assert !Trixi._PREFERENCE_LOOPVECTORIZATION + +trixi_include(joinpath(examples_dir(), "tree_2d_dgsem", "elixir_navierstokes_convergence.jl"), sol = nothing); + + +############################################################################### +# run the simulation + +sol = solve( + ode, + Implicit.RKImplicitExplicitEuler(); + dt = 0.001/2, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, +); + +## dt_vec = [0.001, 0.001/2, 0.0001] +## l2_vec = [4.95311953e-04, 2.48996489e-04 ,5.40458032e-05, ] diff --git a/examples/trixi_navier_stokes_linear_imex.jl b/examples/trixi_navier_stokes_linear_imex.jl new file mode 100644 index 0000000..c115991 --- /dev/null +++ b/examples/trixi_navier_stokes_linear_imex.jl @@ -0,0 +1,35 @@ +# # Using the an implicit solver based on Ariadne with Trixi.jl + +using Trixi +using Implicit +using CairoMakie + + +# Notes: +# Must disable both Polyester and LoopVectorization for Enzyme to be able to differentiate Trixi.jl +# Using https://github.com/trixi-framework/Trixi.jl/pull/2295 +# +# LocalPreferences.jl +# ```toml +# [Trixi] +# loop_vectorization = false +# polyester = false +# ``` + +@assert !Trixi._PREFERENCE_POLYESTER +@assert !Trixi._PREFERENCE_LOOPVECTORIZATION + +trixi_include(joinpath(examples_dir(), "tree_2d_dgsem", "elixir_navierstokes_convergence.jl"), sol = nothing); + +############################################################################### +# run the simulation + +sol = solve( + ode, + Implicit.RKLinearImplicitExplicitEuler(); + dt = 0.001/2, # solve needs some value here but it will be overwritten by the stepsize_callback + ode_default_options()..., callback = callbacks, + # verbose=1, + krylov_algo = :gmres, +); + diff --git a/examples/trixi_rosenbrock.jl b/examples/trixi_rosenbrock.jl new file mode 100644 index 0000000..c530c86 --- /dev/null +++ b/examples/trixi_rosenbrock.jl @@ -0,0 +1,33 @@ +# # Using the an implicit solver based on Ariadne with Trixi.jl + +using Trixi +using Implicit +using CairoMakie + + +# Notes: +# Must disable both Polyester and LoopVectorization for Enzyme to be able to differentiate Trixi.jl +# Using https://github.com/trixi-framework/Trixi.jl/pull/2295 +# +# LocalPreferences.jl +# ```toml +# [Trixi] +# loop_vectorization = false +# polyester = false +# ``` + +@assert !Trixi._PREFERENCE_POLYESTER +@assert !Trixi._PREFERENCE_LOOPVECTORIZATION + +trixi_include(joinpath(examples_dir(), "tree_2d_dgsem", "elixir_advection_basic.jl"), CFL = 10.0, sol = nothing); + +############################################################################### +# run the simulation + +sol = solve( + ode, Implicit.Rosenbrock(); + dt = 1.0, # solve needs some value 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"OpenMPI_jll", "TOML", "Zlib_jll"] +git-tree-sha1 = "cf073e7d4275b8a030140936639f3d6a5eeb3e74" +uuid = "4ee9bed8-4011-53f7-90c2-22363c2f500d" +version = "3.0.1+0" diff --git a/libs/Implicit/Project.toml b/libs/Implicit/Project.toml new file mode 100644 index 0000000..239a4e4 --- /dev/null +++ b/libs/Implicit/Project.toml @@ -0,0 +1,25 @@ +name = "Implicit" +uuid = "7f538e44-2768-4ef2-af90-2110c0378286" +authors = ["Valentin Churavy "] +version = "0.1.0" + +[deps] +Ariadne = "0be81120-40bf-4f8b-adf0-26103efb66f1" +DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e" +Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462" +Trixi = "a7f1ee26-1774-49b1-8366-f1abc58fbfcb" +UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed" + +[sources] +Ariadne = {path = "../.."} + +[compat] +Ariadne = "0.1.0" +DiffEqBase = "6.174.0" +Krylov = "0.10.1" +LinearAlgebra = "1.11.0" +SciMLBase = "2.91.0" +Trixi = "0.12.5" +UnPack = "1.0.2" diff --git a/libs/Implicit/src/Implicit.jl b/libs/Implicit/src/Implicit.jl new file mode 100644 index 0000000..d2f000f --- /dev/null +++ b/libs/Implicit/src/Implicit.jl @@ -0,0 +1,732 @@ +module Implicit + +using UnPack +using Ariadne: Ariadne +using LinearAlgebra +import Ariadne: JacobianOperator +using Krylov + +using Trixi: @trixi_timeit +struct MOperator{JOp} + J::JOp + dt::Float64 +end + +struct LMOperator{JOp} + J::JOp +dt::Float64 +end + +Base.size(M::LMOperator) = size(M.J) +Base.eltype(M::LMOperator) = eltype(M.J) +Base.length(M::LMOperator) = length(M.J) +Base.size(M::MOperator) = size(M.J) +Base.eltype(M::MOperator) = eltype(M.J) +Base.length(M::MOperator) = length(M.J) + +import LinearAlgebra: mul! +function mul!(out::AbstractVector, M::MOperator, v::AbstractVector) + # out = (I/dt - J(f,x,p)) * v + mul!(out, M.J, v) + @. out = v / M.dt - out + return nothing +end + +# Wrapper type for solutions from Implicit.jl's own time integrators, partially mimicking +# SciMLBase.ODESolution +struct TimeIntegratorSolution{tType,uType,P} + t::tType + u::uType + prob::P +end + +# Abstract supertype of Implict.jl's own time integrators for dispatch +abstract type AbstractTimeIntegrator end + +using DiffEqBase: DiffEqBase + +import DiffEqBase: solve, CallbackSet, ODEProblem +export solve, ODEProblem + +# Interface required by DiffEqCallbacks.jl +function DiffEqBase.get_tstops(integrator::AbstractTimeIntegrator) + return integrator.opts.tstops +end +function DiffEqBase.get_tstops_array(integrator::AbstractTimeIntegrator) + return get_tstops(integrator).valtree +end +function DiffEqBase.get_tstops_max(integrator::AbstractTimeIntegrator) + return maximum(get_tstops_array(integrator)) +end + +function finalize_callbacks(integrator::AbstractTimeIntegrator) + callbacks = integrator.opts.callback + + return if callbacks isa CallbackSet + foreach(callbacks.discrete_callbacks) do cb + cb.finalize(cb, integrator.u, integrator.t, integrator) + end + foreach(callbacks.continuous_callbacks) do cb + cb.finalize(cb, integrator.u, integrator.t, integrator) + end + end +end + +import SciMLBase: get_du, get_tmp_cache, u_modified!, + init, step!, check_error, + get_proposed_dt, set_proposed_dt!, + terminate!, remake, add_tstop!, has_tstop, first_tstop + + +# Abstract base type for time integration schemes +abstract type SimpleImplicitAlgorithm{N} end +abstract type NonDirect{N} <: SimpleImplicitAlgorithm{N} end +abstract type Direct{N} <: SimpleImplicitAlgorithm{N} end + +stages(::SimpleImplicitAlgorithm{N}) where {N} = N + +struct ImplicitEuler <: NonDirect{1} end +function (::ImplicitEuler)(res, uₙ, Δt, f!, du, u, p, t, stages, stage) + f!(du, u, p, t + Δt) # t = t0 + c_1 * Δt + + res .= uₙ .+ Δt .* du .- u # Δt * a_11 + return nothing +end + +struct ImplicitMidpoint <: SimpleImplicitAlgorithm{1} end +function (::ImplicitMidpoint)(res, uₙ, Δt, f!, du, u, p, t, stages, stage) + # Evaluate f at midpoint: f((uₙ + u)/2, t + Δt/2) + # Use res for a temporary allocation (uₙ .+ u) ./ 2 + uuₙ = res + uuₙ .= 0.5 .* (uₙ .+ u) + f!(du, uuₙ, p, t + 0.5 * Δt) + + res .= uₙ .+ Δt .* du .- u + return nothing +end + +struct ImplicitTrapezoid <: SimpleImplicitAlgorithm{1} end +function (::ImplicitTrapezoid)(res, uₙ, Δt, f!, du, u, p, t, stages, stage) + # Need to evaluate f at both endpoints + # f(uₙ, t) and f(u, t + Δt) + # Use res as the temporary for duₙ = f(uₙ, t) + duₙ = res + f!(duₙ, uₙ, p, t) + f!(du, u, p, t + Δt) + + res .= uₙ .+ (Δt / 2) .* (duₙ .+ du) .- u + return nothing +end + +""" + TRBDF2 + +TR-BDF2 based solver after [Bank1985-gh](@cite). +Using the formula given in [Bonaventura2021-za](@cite) eq (1). +See [Hosea1996-xv](@cite) for how it relates to implicit RK methods +""" +struct TRBDF2 <: SimpleImplicitAlgorithm{2} end +function (::TRBDF2)(res, uₙ, Δt, f!, du, u, p, t, stages, stage) + γ = 2 - √2 + return if stage == 1 + # Stage 1: Trapezoidal rule to t + γΔt + # u here is u₁ candidate + duₙ = res + f!(duₙ, uₙ, p, t) + f!(du, u, p, t + γ * Δt) + + res .= uₙ .+ ((γ / 2) * Δt) .* (duₙ .+ du) .- u + else + # Stage 2: BDF2 from t + γΔt to t + Δt + # Note these are unequal timestep + f!(du, u, p, t + Δt) + + u₁ = stages[1] + + # Bank1985 defines in eq 32 + # (2-γ)u + (1-γ)Δt * f(u, t+Δt) = 1/γ * u₁ - 1/γ * (1-γ)^2 * uₙ + # Manual derivation (devision by (2-γ) and then move everything to one side.) + # a₁ = -((1 - γ)^2) / (γ * (2 - γ)) + # a₂ = 1 / (γ * (2 - γ)) + # a₃ = - (1 - γ) / (2 - γ) + # res .= a₁ .* uₙ .+ a₂ .* u₁ .+ a₃ .* Δt .* du .- u + + # after Bonaventura2021 + # They define the second stage as: + # u - γ₂ * Δt * f(u, t+Δt) = (1-γ₃)uₙ + γ₃u₁ + # Which differs from Bank1985) + # (2-γ)u + (1-γ)Δt * f(u, t+Δt) = 1/γ * u₁ - 1/γ * (1-γ)^2 * uₙ + # In the sign of u - γ₂ * Δt + # a₁ == (1-γ₃) + # a₂ == γ₃ + # a₃ == -γ₂ + γ₂ = (1 - γ) / (2 - γ) + γ₃ = 1 / (γ * (2 - γ)) + + res .= (1 - γ₃) .* uₙ .+ γ₃ .* u₁ + (γ₂ * Δt) .* du .- u + end +end + +abstract type DIRK{N} <: SimpleImplicitAlgorithm{N} end + +struct RKImplicitEuler <: DIRK{1} end + +function (::RKImplicitEuler)(res, uₙ, Δt, f!, du, u, p, t, stages, stage, RK) + if stage == 1 + # Stage 1: + f!(du, u, p, t + RK.c[stage] * Δt) + return res .= u .- uₙ .- RK.a[stage, stage] * Δt .* du + else + @. u = uₙ + RK.b[1] * Δt * stages[1] + end + +end + +struct KS22 <: DIRK{2} end +struct QZ22 <: DIRK{2} end +struct C23 <: DIRK{2} end + +function (::DIRK{2})(res, uₙ, Δt, f!, du, u, p, t, stages, stage, RK) + if stage == 1 + f!(du, u, p, t + RK.c[stage] * Δt) + return res .= u .- uₙ .- RK.a[stage, stage] * Δt .* du + elseif stage == 2 + f!(du, u, p, t + RK.c[stage] * Δt) + return res .= u .- uₙ .- RK.a[stage, 1] * Δt .* stages[1] - RK.a[stage, 2] * Δt .* du + else + @. u = uₙ + Δt * (RK.b[1] * stages[1] + RK.b[2] * stages[2]) + end + +end + +struct C34 <: DIRK{3} end +struct L33 <: DIRK{3} end + +struct RKTRBDF2 <: DIRK{3} end + +function (::DIRK{3})(res, uₙ, Δt, f!, du, u, p, t, stages, stage, RK) + if stage == 1 + f!(du, u, p, t + RK.c[stage] * Δt) + return res .= u .- uₙ .- RK.a[stage, 1] * Δt .* du + elseif stage == 2 + f!(du, u, p, t + RK.c[stage] * Δt) + return res .= u .- uₙ .- RK.a[stage, 1] * Δt .* stages[1] - RK.a[stage, 2] * Δt .* du + elseif stage == 3 + f!(du, u, p, t + RK.c[stage] * Δt) + return res .= u .- uₙ .- RK.a[stage, 1] * Δt .* stages[1] - RK.a[stage, 2] * Δt .* stages[2] - RK.a[stage, 3] * Δt .* du + else + @. u = uₙ + Δt * (RK.b[1] * stages[1] + RK.b[2] * stages[2] + RK.b[3] * stages[3]) + end + +end + +struct Rosenbrock <: Direct{3} end + +function (::Rosenbrock)(res, uₙ, Δt, f!, du, u, p, t, stages, stage, workspace, M, RK) + invdt = inv(Δt) + @. u = uₙ + @. res = 0 + for j in 1:(stage-1) + @. u = u + RK.a[stage, j] * stages[j] + @. res = res + RK.c[stage, j] * stages[j] * invdt + end + + ## It does not work for non-autonomous systems. + f!(du, u, p, t + Δt) + + krylov_solve!(workspace, M, copy(du .+ res)) + stages[stage] .= workspace.x + + if stage == 3 + @. u = uₙ + for j in 1:stage + @. u = u + RK.m[j] * stages[j] + end + end + +end +abstract type RKTableau end + +struct RosenbrockButcher{T1<:AbstractArray,T2<:AbstractArray} <: RKTableau + a::T1 + c::T1 + m::T2 +end + +struct DIRKButcher{T1<:AbstractArray,T2<:AbstractArray} <: RKTableau + a::T1 + b::T2 + c::T2 +end + +function RosenbrockTableau() + + # SSP - Knoth + nstage = 3 + alpha = zeros(Float64, nstage, nstage) + alpha[2, 1] = 1 + alpha[3, 1] = 1 / 4 + alpha[3, 2] = 1 / 4 + + b = zeros(Float64, nstage) + b[1] = 1 / 6 + b[2] = 1 / 6 + b[3] = 2 / 3 + + gamma = zeros(Float64, nstage, nstage) + gamma[1, 1] = 1 + gamma[2, 2] = 1 + gamma[3, 1] = -3 / 4 + gamma[3, 2] = -3 / 4 + gamma[3, 3] = 1 + + a = alpha * inv(gamma) + m = transpose(b) * inv(gamma) + c = diagm(inv.(diag(gamma))) - inv(gamma) + return RosenbrockButcher(a, c, vec(m)) + +end + +function ImplicitEulerTableau() + + nstage = 1 + a = zeros(Float64, nstage, nstage) + a[1, 1] = 1 + + b = zeros(Float64, nstage) + b[1] = 1 + + c = zeros(Float64, nstage) + c[1] = 1 + return DIRKButcher(a, b, c) +end + +# Kraaijevanger and Spijker's two-stage Diagonally Implicit Runge–Kutta method: +function KS22Tableau() + nstage = 2 + a = zeros(Float64, nstage, nstage) + a[1, 1] = 1 / 2 + a[2, 1] = -1 / 2 + a[2, 2] = 2 + b = zeros(Float64, nstage) + b[1] = -1 / 2 + b[2] = 3 / 2 + + c = zeros(Float64, nstage) + c[1] = 1 / 2 + c[2] = 3 / 2 + return DIRKButcher(a, b, c) + +end + +# Qin and Zhang's two-stage, 2nd order, symplectic Diagonally Implicit Runge–Kutta method: +function QZ22Tableau() + nstage = 2 + a = zeros(Float64, nstage, nstage) + a[1, 1] = 1 / 4 + a[2, 1] = 1 / 2 + a[2, 2] = 1 / 4 + b = zeros(Float64, nstage) + b[1] = 1 / 2 + b[2] = 1 / 2 + + c = zeros(Float64, nstage) + c[1] = 1 / 4 + c[2] = 3 / 4 + return DIRKButcher(a, b, c) +end + +# Crouzeix's two-stage, 3rd order Diagonally Implicit Runge–Kutta method +function C23Tableau() + nstage = 2 + a = zeros(Float64, nstage, nstage) + a[1, 1] = 1 / 2 + sqrt(3) / 6 + a[2, 1] = -sqrt(3) / 3 + a[2, 2] = 1 / 2 + sqrt(3) / 6 + b = zeros(Float64, nstage) + b[1] = 1 / 2 + b[2] = 1 / 2 + + c = zeros(Float64, nstage) + c[1] = 1 / 2 + sqrt(3) / 6 + c[2] = 1 / 2 - sqrt(3) / 6 + return DIRKButcher(a, b, c) +end +# Crouzeix's three-stage, 4th order Diagonally Implicit Runge–Kutta method: +function C34Tableau() + nstage = 3 + alpha = 2 / sqrt(3) * cospi(1 / 18) + a = zeros(Float64, nstage, nstage) + a[1, 1] = (1 + alpha) / 2 + a[2, 1] = -alpha / 2 + a[2, 2] = a[1, 1] + a[3, 1] = 1 + alpha + a[3, 2] = -(1 + 2 * alpha) + a[3, 3] = (1 + alpha) / 2 + b = zeros(Float64, nstage) + b[1] = 1 / (6 * alpha^2) + b[2] = 1 - 1 / (3 * alpha^2) + b[3] = 1 / (6 * alpha^2) + + c = zeros(Float64, nstage) + c[1] = a[1, 1] + c[2] = a[2, 1] + a[2, 2] + c[3] = a[3, 1] + a[3, 2] + a[3, 3] + return DIRKButcher(a, b, c) +end + +# L-Stable third order, FSAL! It can be optmized, because of the FSAL. +function L33Tableau() + nstage = 3 + x = 0.4368665215 + alpha = 2 / sqrt(3) * cospi(1 / 18) + a = zeros(Float64, nstage, nstage) + a[1, 1] = x + a[2, 1] = (1 - x) / 2 + a[2, 2] = x + a[3, 1] = -3 * x^2 / 2 + 4 * x - 1 / 4 + a[3, 2] = 3 * x^2 / 2 - 5 * x + 5 / 4 + a[3, 3] = x + b = zeros(Float64, nstage) + b[1] = a[3, 1] + b[2] = a[3, 2] + b[3] = a[3, 3] + + c = zeros(Float64, nstage) + c[1] = a[1, 1] + c[2] = a[2, 1] + a[2, 2] + c[3] = a[3, 1] + a[3, 2] + a[3, 3] + return DIRKButcher(a, b, c) +end + +function TRBDF2Tableau() + nstage = 3 + gamma = 2 - sqrt(2) + a = zeros(Float64, nstage, nstage) + a[2,1] = gamma/2 + a[2,2] = a[2,1] + a[3,1] = 1/(2*(2-gamma)) + a[3,2] = a[3,1] + a[3,3] = (1-gamma)/(2-gamma) + + b = zeros(Float64, nstage) + b[1] = a[3, 1] + b[2] = a[3, 2] + b[3] = a[3, 3] + + c = zeros(Float64, nstage) + c[1] = a[1, 1] + c[2] = a[2, 1] + a[2, 2] + c[3] = a[3, 1] + a[3, 2] + a[3, 3] + return DIRKButcher(a, b, c) +end + +function RKTableau(alg::Direct) + return RosenbrockTableau() +end + +function RKTableau(alg::NonDirect) + return RosenbrockTableau() +end + +function RKTableau(alg::RKImplicitEuler) + return ImplicitEulerTableau() +end + +function RKTableau(alg::KS22) + return KS22Tableau() +end + +function RKTableau(alg::QZ22) + return QZ22Tableau() +end + +function RKTableau(alg::C23) + return C23Tableau() +end + +function RKTableau(alg::C34) + return C34Tableau() +end + +function RKTableau(alg::L33) + return L33Tableau() +end + +function RKTableau(alg::RKTRBDF2) + return TRBDF2Tableau() +end + +function nonlinear_problem(alg::SimpleImplicitAlgorithm, f::F) where {F} + return (res, u, (uₙ, Δt, du, p, t, stages, stage)) -> alg(res, uₙ, Δt, f, du, u, p, t, stages, stage) +end + +function nonlinear_problem(alg::DIRK, f::F) where {F} + return (res, u, (uₙ, Δt, du, p, t, stages, stage, RK)) -> alg(res, uₙ, Δt, f, du, u, p, t, stages, stage, RK) +end + +# This struct is needed to fake https://github.com/SciML/OrdinaryDiffEq.jl/blob/0c2048a502101647ac35faabd80da8a5645beac7/src/integrators/type.jl#L1 +mutable struct SimpleImplicitOptions{Callback} + callback::Callback # callbacks; used in Trixi.jl + adaptive::Bool # whether the algorithm is adaptive; ignored + dtmax::Float64 # ignored + maxiters::Int # maximal number of time steps + tstops::Vector{Float64} # tstops from https://diffeq.sciml.ai/v6.8/basics/common_solver_opts/#Output-Control-1; ignored + verbose::Int + algo::Symbol + krylov_kwargs::Any +end + + +function SimpleImplicitOptions(callback, tspan; maxiters=typemax(Int), verbose=0, krylov_algo=:gmres, krylov_kwargs=(;), kwargs...) + return SimpleImplicitOptions{typeof(callback)}( + callback, false, Inf, maxiters, + [last(tspan)], + verbose, + krylov_algo, + krylov_kwargs, + ) +end + +# This struct is needed to fake https://github.com/SciML/OrdinaryDiffEq.jl/blob/0c2048a502101647ac35faabd80da8a5645beac7/src/integrators/type.jl#L77 +# This implements the interface components described at +# https://diffeq.sciml.ai/v6.8/basics/integrator/#Handing-Integrators-1 +# which are used in Trixi.jl. +mutable struct SimpleImplicit{ + RealT<:Real,uType,Params,Sol,F,M,Alg<:SimpleImplicitAlgorithm, + SimpleImplicitOptions,RKTableau, +} <: AbstractTimeIntegrator + u::uType + du::uType + u_tmp::uType + stages::NTuple{M,uType} + res::uType + t::RealT + dt::RealT # current time step + dtcache::RealT # ignored + iter::Int # current number of time steps (iteration) + p::Params # will be the semidiscretization from Trixi.jl + sol::Sol # faked + f::F # `rhs!` of the semidiscretization + alg::Alg # SimpleImplicitAlgorithm + opts::SimpleImplicitOptions + finalstep::Bool # added for convenience + RK::RKTableau +end + +# Forward integrator.stats.naccept to integrator.iter (see GitHub PR#771) +function Base.getproperty(integrator::SimpleImplicit, field::Symbol) + if field === :stats + return (naccept=getfield(integrator, :iter),) + end + # general fallback + return getfield(integrator, field) +end + +function init( + ode::ODEProblem, alg::SimpleImplicitAlgorithm{N}; + dt, callback::Union{CallbackSet,Nothing}=nothing, kwargs..., +) where {N} + u = copy(ode.u0) + du = zero(u) + res = zero(u) + u_tmp = similar(u) + stages = ntuple(_ -> similar(u), Val(N)) + t = first(ode.tspan) + iter = 0 + integrator = SimpleImplicit( + u, du, u_tmp, stages, res, t, dt, zero(dt), iter, ode.p, + (prob=ode,), ode.f, alg, + SimpleImplicitOptions( + callback, ode.tspan; + kwargs..., + ), false, RKTableau(alg)) + + # initialize callbacks + if callback isa CallbackSet + foreach(callback.continuous_callbacks) do cb + throw(ArgumentError("Continuous callbacks are unsupported with the implicit time integration methods.")) + end + foreach(callback.discrete_callbacks) do cb + cb.initialize(cb, integrator.u, integrator.t, integrator) + end + end + + return integrator +end + +# Fakes `solve`: https://diffeq.sciml.ai/v6.8/basics/overview/#Solving-the-Problems-1 +function solve( + ode::ODEProblem, alg::SimpleImplicitAlgorithm; + dt, callback=nothing, kwargs..., +) + integrator = init(ode, alg, dt=dt, callback=callback; kwargs...) + + # Start actual solve + return solve!(integrator) +end + +function solve!(integrator::SimpleImplicit) + @unpack prob = integrator.sol + + integrator.finalstep = false + + while !integrator.finalstep + step!(integrator) + end # "main loop" timer + + finalize_callbacks(integrator) + + return TimeIntegratorSolution( + (first(prob.tspan), integrator.t), + (prob.u0, integrator.u), + integrator.sol.prob, + ) +end + +function stage!(integrator, alg::NonDirect) + for stage in 1:stages(alg) + F! = nonlinear_problem(alg, integrator.f) + # TODO: Pass in `stages[1:(stage-1)]` or full tuple? + _, stats = Ariadne.newton_krylov!( + F!, integrator.u_tmp, (integrator.u, integrator.dt, integrator.du, integrator.p, integrator.t, integrator.stages, stage), integrator.res; + verbose=integrator.opts.verbose, krylov_kwargs=integrator.opts.krylov_kwargs, + algo=integrator.opts.algo, tol_abs=6.0e-6, + ) + @assert stats.solved + if stage < stages(alg) + # Store the solution for each stage in stages + integrator.stages[stage] .= integrator.u_tmp + end + end +end + +function stage!(integrator, alg::DIRK) + for stage in 1:stages(alg) + F! = nonlinear_problem(alg, integrator.f) + # TODO: Pass in `stages[1:(stage-1)]` or full tuple? + _, stats = Ariadne.newton_krylov!( + F!, integrator.u_tmp, (integrator.u, integrator.dt, integrator.du, integrator.p, integrator.t, integrator.stages, stage, integrator.RK), integrator.res; + verbose=integrator.opts.verbose, krylov_kwargs=integrator.opts.krylov_kwargs, + algo=integrator.opts.algo, tol_abs=6.0e-6, + ) + @assert stats.solved + + # Store the solution for each stage in stages + integrator.f(integrator.du, integrator.u_tmp, integrator.p, integrator.t + integrator.RK.c[stage] * integrator.dt) + integrator.stages[stage] .= integrator.du + if stage == stages(alg) + alg(integrator.res, integrator.u, integrator.dt, integrator.f, integrator.du, integrator.u_tmp, integrator.p, integrator.t, integrator.stages, stage + 1, integrator.RK) + end + + end +end + +function stage!(integrator, alg::Direct) + + F!(du, u, p) = integrator.f(du, u, p, integrator.t) + J = JacobianOperator(F!, integrator.du, integrator.u, integrator.p) + M = MOperator(J, integrator.dt) + kc = KrylovConstructor(integrator.res) + workspace = krylov_workspace(:gmres, kc) + + for stage in 1:stages(alg) + alg(integrator.res, integrator.u, integrator.dt, integrator.f, integrator.du, integrator.u_tmp, integrator.p, integrator.t, integrator.stages, stage, workspace, M, integrator.RK) + end + +end + +function step!(integrator::SimpleImplicit) + @unpack prob = integrator.sol + @unpack alg = integrator + t_end = last(prob.tspan) + callbacks = integrator.opts.callback + + @assert !integrator.finalstep + if isnan(integrator.dt) + error("time step size `dt` is NaN") + end + + # if the next iteration would push the simulation beyond the end time, set dt accordingly + if integrator.t + integrator.dt > t_end || + isapprox(integrator.t + integrator.dt, t_end) + integrator.dt = t_end - integrator.t + terminate!(integrator) + end + + # one time step + integrator.u_tmp .= integrator.u + + stage!(integrator, alg) + + integrator.u .= integrator.u_tmp + + integrator.iter += 1 + integrator.t += integrator.dt + + begin + # handle callbacks + if callbacks isa CallbackSet + foreach(callbacks.discrete_callbacks) do cb + if cb.condition(integrator.u, integrator.t, integrator) + cb.affect!(integrator) + end + return nothing + end + end + end + + # respect maximum number of iterations + return if integrator.iter >= integrator.opts.maxiters && !integrator.finalstep + @warn "Interrupted. Larger maxiters is needed." + terminate!(integrator) + end +end + +# get a cache where the RHS can be stored +get_du(integrator::SimpleImplicit) = integrator.du +get_tmp_cache(integrator::SimpleImplicit) = (integrator.u_tmp,) + +# some algorithms from DiffEq like FSAL-ones need to be informed when a callback has modified u +u_modified!(integrator::SimpleImplicit, ::Bool) = false + +# used by adaptive timestepping algorithms in DiffEq +function set_proposed_dt!(integrator::SimpleImplicit, dt) + return integrator.dt = dt +end + +# Required e.g. for `glm_speed_callback` +function get_proposed_dt(integrator::SimpleImplicit) + return integrator.dt +end + +# stop the time integration +function terminate!(integrator::SimpleImplicit) + integrator.finalstep = true + return empty!(integrator.opts.tstops) +end + +# used for AMR +function Base.resize!(integrator::SimpleImplicit, new_size) + resize!(integrator.u, new_size) + resize!(integrator.du, new_size) + return resize!(integrator.u_tmp, new_size) +end + +### Helper +jacobian(G!, ode::ODEProblem, Δt) = jacobian(G!, ode.f, ode.u0, ode.p, Δt, first(ode.tspan)) + +function jacobian(G!, f!, uₙ, p, Δt, t) + u = copy(uₙ) + du = zero(uₙ) + res = zero(uₙ) + + F! = nonlinear_problem(G!, f!) + + J = Ariadne.JacobianOperator(F!, res, u, (uₙ, Δt, du, p, t)) + return collect(J) +end + +include("imex.jl") +include("linear_imex.jl") +end # module Implicit diff --git a/libs/Implicit/src/imex.jl b/libs/Implicit/src/imex.jl new file mode 100644 index 0000000..41f1f77 --- /dev/null +++ b/libs/Implicit/src/imex.jl @@ -0,0 +1,263 @@ + +abstract type SimpleImplicitExplicitAlgorithm{N} end + +abstract type RKIMEX{N} <: SimpleImplicitExplicitAlgorithm{N} end + +struct RKImplicitExplicitEuler <: RKIMEX{1} end + +function (::RKImplicitExplicitEuler)(res, uₙ, Δt, f1!, f2!, du, du_tmp, u, p, t, stages, stage, RK) + if stage == 1 + # Stage 1: + ## f2 is the conservative part + ## f1 is the parabolic part + f2!(du, uₙ, p, t + RK.c[stage] * Δt ) + f1!(du_tmp, u, p, t + RK.c[stage] * Δt ) + return res .= u .- uₙ .- RK.a[stage, stage] * Δt .* du - RK.a[stage,stage] * Δt * du_tmp + else + @. u = uₙ + RK.b[1] * Δt * stages[1] + end + +end + +stages(::SimpleImplicitExplicitAlgorithm{N}) where {N} = N + +function nonlinear_problem(alg::SimpleImplicitExplicitAlgorithm, f2::F2) where {F2} + return (res, u, (uₙ, Δt, f1, du, du_tmp, p, t, stages, stage, RK)) -> alg(res, uₙ, Δt, f1, f2, du, du_tmp, u, p, t, stages, stage, RK) +end + +mutable struct SimpleImplicitExplicitOptions{Callback} + callback::Callback # callbacks; used in Trixi.jl + adaptive::Bool # whether the algorithm is adaptive; ignored + dtmax::Float64 # ignored + maxiters::Int # maximal number of time steps + tstops::Vector{Float64} # tstops from https://diffeq.sciml.ai/v6.8/basics/common_solver_opts/#Output-Control-1; ignored + verbose::Int + algo::Symbol + krylov_kwargs::Any +end + +function RKTableau(alg::RKImplicitExplicitEuler) + return ImplicitExplicitEulerTableau() +end + +function ImplicitExplicitEulerTableau() + + nstage = 1 + a = zeros(Float64, nstage, nstage) + a[1, 1] = 1 + + b = zeros(Float64, nstage) + b[1] = 1 + + c = zeros(Float64, nstage) + c[1] = 1 + return DIRKButcher(a, b, c) +end + + +function SimpleImplicitExplicitOptions(callback, tspan; maxiters=typemax(Int), verbose=0, krylov_algo=:gmres, krylov_kwargs=(;), kwargs...) + return SimpleImplicitExplicitOptions{typeof(callback)}( + callback, false, Inf, maxiters, + [last(tspan)], + verbose, + krylov_algo, + krylov_kwargs, + ) +end + +mutable struct SimpleImplicitExplicit{ + RealT<:Real,uType,Params,Sol,F,F1,F2,M,Alg<:SimpleImplicitExplicitAlgorithm, + SimpleImplicitExplicitOptions,RKTableau, +} <: AbstractTimeIntegrator + u::uType + du::uType + du_tmp::uType + u_tmp::uType + stages::NTuple{M,uType} + res::uType + t::RealT + dt::RealT # current time step + dtcache::RealT # ignored + iter::Int # current number of time steps (iteration) + p::Params # will be the semidiscretization from Trixi.jl + sol::Sol # faked + f::F #TODO: that should be sum of f1 and f2 + f1::F1 # `rhs!` parabolic + f2::F2 # rhs! conservative + alg::Alg # SimpleImplicitAlgorithm + opts::SimpleImplicitExplicitOptions + finalstep::Bool # added for convenience + RK::RKTableau +end + + +function Base.getproperty(integrator::SimpleImplicitExplicit, field::Symbol) + if field === :stats + return (naccept=getfield(integrator, :iter),) + end + # general fallback + return getfield(integrator, field) +end + +function init( + ode::ODEProblem, alg::SimpleImplicitExplicitAlgorithm{N}; + dt, callback::Union{CallbackSet,Nothing}=nothing, kwargs..., +) where {N} + u = copy(ode.u0) + du = zero(u) + res = zero(u) + u_tmp = similar(u) + stages = ntuple(_ -> similar(u), Val(N)) + t = first(ode.tspan) + iter = 0 + integrator = SimpleImplicitExplicit( + u, du, copy(du), u_tmp, stages, res, t, dt, zero(dt), iter, ode.p, + (prob=ode,), ode.f.f1, ode.f.f1, ode.f.f2, alg, + SimpleImplicitExplicitOptions( + callback, ode.tspan; + kwargs..., + ), false, RKTableau(alg)) + + # initialize callbacks + if callback isa CallbackSet + foreach(callback.continuous_callbacks) do cb + throw(ArgumentError("Continuous callbacks are unsupported with the implicit time integration methods.")) + end + foreach(callback.discrete_callbacks) do cb + cb.initialize(cb, integrator.u, integrator.t, integrator) + end + end + + return integrator +end + +# Fakes `solve`: https://diffeq.sciml.ai/v6.8/basics/overview/#Solving-the-Problems-1 +function solve( + ode::ODEProblem, alg::SimpleImplicitExplicitAlgorithm; + dt, callback=nothing, kwargs..., +) + integrator = init(ode, alg, dt=dt, callback=callback; kwargs...) + + # Start actual solve + return solve!(integrator) +end + +function solve!(integrator::SimpleImplicitExplicit) + @unpack prob = integrator.sol + + integrator.finalstep = false + + while !integrator.finalstep + step!(integrator) + end # "main loop" timer + + finalize_callbacks(integrator) + + return TimeIntegratorSolution( + (first(prob.tspan), integrator.t), + (prob.u0, integrator.u), + integrator.sol.prob, + ) +end + + +function step!(integrator::SimpleImplicitExplicit) + @unpack prob = integrator.sol + @unpack alg = integrator + t_end = last(prob.tspan) + callbacks = integrator.opts.callback + + @assert !integrator.finalstep + if isnan(integrator.dt) + error("time step size `dt` is NaN") + end + + # if the next iteration would push the simulation beyond the end time, set dt accordingly + if integrator.t + integrator.dt > t_end || + isapprox(integrator.t + integrator.dt, t_end) + integrator.dt = t_end - integrator.t + terminate!(integrator) + end + + # one time step + integrator.u_tmp .= integrator.u + + stage!(integrator, alg) + + integrator.u .= integrator.u_tmp + + integrator.iter += 1 + integrator.t += integrator.dt + + begin + # handle callbacks + if callbacks isa CallbackSet + foreach(callbacks.discrete_callbacks) do cb + if cb.condition(integrator.u, integrator.t, integrator) + cb.affect!(integrator) + end + return nothing + end + end + end + + # respect maximum number of iterations + return if integrator.iter >= integrator.opts.maxiters && !integrator.finalstep + @warn "Interrupted. Larger maxiters is needed." + terminate!(integrator) + end +end + + +function stage!(integrator, alg::RKIMEX) + for stage in 1:stages(alg) + F! = nonlinear_problem(alg, integrator.f2) + # TODO: Pass in `stages[1:(stage-1)]` or full tuple? + _, stats = Ariadne.newton_krylov!( + F!, integrator.u_tmp, (integrator.u, integrator.dt, integrator.f1, integrator.du, integrator.du_tmp, integrator.p, integrator.t, integrator.stages, stage, integrator.RK), integrator.res; + verbose=integrator.opts.verbose, krylov_kwargs=integrator.opts.krylov_kwargs, + algo=integrator.opts.algo, tol_abs=6.0e-6, + ) + @assert stats.solved + # Store the solution for each stage in stages + ## For a split Problem we need to compute rhs_conservative and rhs_parabolic + integrator.f2(integrator.du, integrator.u_tmp, integrator.p, integrator.t + integrator.RK.c[stage] * integrator.dt) + integrator.stages[stage] .= integrator.du + integrator.f1(integrator.du, integrator.u_tmp, integrator.p, integrator.t + integrator.RK.c[stage] * integrator.dt) + integrator.stages[stage] .+= integrator.du + if stage == stages(alg) + alg(integrator.res, integrator.u, integrator.dt, integrator.f1, integrator.f2, integrator.du, integrator.du_tmp, integrator.u_tmp, integrator.p, integrator.t, integrator.stages, stage + 1, integrator.RK) + end + + end +end + +# get a cache where the RHS can be stored +get_du(integrator::SimpleImplicitExplicit) = integrator.du +get_tmp_cache(integrator::SimpleImplicitExplicit) = (integrator.u_tmp,) + +# some algorithms from DiffEq like FSAL-ones need to be informed when a callback has modified u +u_modified!(integrator::SimpleImplicitExplicit, ::Bool) = false + +# used by adaptive timestepping algorithms in DiffEq +function set_proposed_dt!(integrator::SimpleImplicitExplicit, dt) + return integrator.dt = dt +end + +# Required e.g. for `glm_speed_callback` +function get_proposed_dt(integrator::SimpleImplicitExplicit) + return integrator.dt +end + +# stop the time integration +function terminate!(integrator::SimpleImplicitExplicit) + integrator.finalstep = true + return empty!(integrator.opts.tstops) +end + +# used for AMR +function Base.resize!(integrator::SimpleImplicitExplicit, new_size) + resize!(integrator.u, new_size) + resize!(integrator.du, new_size) + return resize!(integrator.u_tmp, new_size) +end diff --git a/libs/Implicit/src/linear_imex.jl b/libs/Implicit/src/linear_imex.jl new file mode 100644 index 0000000..e2aa144 --- /dev/null +++ b/libs/Implicit/src/linear_imex.jl @@ -0,0 +1,379 @@ +abstract type SimpleLinearImplicitExplicitAlgorithm{N} end + +abstract type RKLIMEX{N} <: SimpleLinearImplicitExplicitAlgorithm{N} end + + +struct IMEXRKButcher{T1<:AbstractArray,T2<:AbstractArray} <: RKTableau + a::T1 + b::T2 + c::T2 + ah::T1 + bh::T2 + ch::T2 +end + +struct RKLinearImplicitExplicitEuler <: RKLIMEX{1} end + +struct RKLSSPIMEX332 <: RKLIMEX{3} end + +function mul!(out::AbstractVector, M::LMOperator, v::AbstractVector) + # out = (I/dt - J(f,x,p)) * v + mul!(out, M.J, v) + @. out = v - out * M.dt + return nothing +end + +function (::RKLinearImplicitExplicitEuler)(res, uₙ, Δt, f1!, f2!, du, du_tmp, u, p, t, stages, ustages, jstages, stage, RK, M, lin_du_tmp, lin_du_tmp1, workspace) + if stage == 1 + # Stage 1: + ## f2 is the conservative part + ## f1 is the parabolic part + mul!(lin_du_tmp, M.J, uₙ) +# mul!(lin_du_tmp1, J, u) + f2!(du, uₙ, p, t + RK.c[stage] * Δt) + f1!(du_tmp, uₙ, p, t + RK.c[stage] * Δt) + + res .= uₙ .+ RK.a[stage, stage] * Δt .* (du .+ du_tmp .- lin_du_tmp) + krylov_solve!(workspace, M, res, atol = 1e-6, rtol = 1e-6) + @. u = workspace.x +# f2!(du, workspace.x, p, t + RK.c[stage] * Δt) +# f1!(du_tmp, workspace.x, p, t + RK.c[stage] * Δt) +# stages[stage] .= du .+ du_tmp +# @. u = uₙ + RK.b[1] * Δt * stages[1] + end +end + + +function (::RKLIMEX{3})(res, uₙ, Δt, f1!, f2!, du, du_tmp, u, p, t, stages, ustages, jstages, stage, RK, M, lin_du_tmp, lin_du_tmp1, workspace) + F!(du, u, p) = f1!(du, u, p, t) ## parabolic + if stage == 1 + # Stage 1: + ## f2 is the conservative part + ## f1 is the parabolic part + J = JacobianOperator(F!, du, uₙ, p) + M = LMOperator(J, RK.ah[stage,stage] * Δt) + krylov_solve!(workspace, M, uₙ, atol = 1e-6, rtol = 1e-6) + @. u = workspace.x + J = JacobianOperator(F!, du, u, p) + mul!(jstages[stage], J, u) + + f2!(du, workspace.x, p, t + RK.c[stage] * Δt) + f1!(du_tmp, workspace.x, p, t + RK.c[stage] * Δt) + stages[stage] .= du .+ du_tmp - jstages[stage] + ustages[stage] .= u +# @. u = uₙ + RK.b[1] * Δt * stages[1] + elseif stage == 2 + + J = JacobianOperator(F!, du, ustages[1], p) + M = LMOperator(J, RK.ah[stage,stage] * Δt) + mul!(lin_du_tmp, M.J, uₙ) +# mul!(lin_du_tmp1, J, u) + res .= uₙ + RK.a[stage,1] * Δt * stages[1] - Δt * RK.ah[stage,1] * jstages[1] + + krylov_solve!(workspace, M, res, atol = 1e-6, rtol = 1e-6) + @. u = workspace.x + J = JacobianOperator(F!, du, u, p) + mul!(jstages[stage], J, u) + f2!(du, workspace.x, p, t + RK.c[stage] * Δt) + f1!(du_tmp, workspace.x, p, t + RK.c[stage] * Δt) + stages[stage] .= du .+ du_tmp - jstages[stage] + ustages[stage] .= u + + elseif stage == 3 + + J = JacobianOperator(F!, du, ustages[2], p) + M = LMOperator(J, RK.ah[stage,stage] * Δt) + mul!(lin_du_tmp, M.J, uₙ) +# mul!(lin_du_tmp1, J, u) + res .= uₙ + RK.a[stage,1] * Δt * stages[1] + RK.a[stage,2] * Δt * stages[2] - Δt * RK.ah[stage,1] * jstages[1] - Δt * RK.ah[stage,2] * jstages[2] + krylov_solve!(workspace, M, res, atol = 1e-6, rtol = 1e-6) + @. u = workspace.x + J = JacobianOperator(F!, du, u, p) + mul!(jstages[stage], J, u) + f2!(du, workspace.x, p, t + RK.c[stage] * Δt) + f1!(du_tmp, workspace.x, p, t + RK.c[stage] * Δt) + stages[stage] .= du .+ du_tmp - jstages[stage] + ustages[stage] .= u + + @. u = uₙ + RK.b[1] * Δt * stages[1] + RK.b[2] * Δt * stages[2] + RK.b[3] * Δt * stages[3] - RK.bh[1] * Δt * jstages[1] - RK.bh[2] * Δt * jstages[2] - RK.bh[3] * Δt * jstages[3] + end +end + +stages(::SimpleLinearImplicitExplicitAlgorithm{N}) where {N} = N + +function nonlinear_problem(alg::SimpleLinearImplicitExplicitAlgorithm, f2::F2) where {F2} + return (res, u, (uₙ, Δt, f1, du, du_tmp, p, t, stages, stage, RK, J, lin_du_tmp, lin_du_tmp1)) -> alg(res, uₙ, Δt, f1, f2, du, du_tmp, u, p, t, stages, stage, RK, J, lin_du_tmp, lin_du_tmp1) +end + +mutable struct SimpleLinearImplicitExplicitOptions{Callback} + callback::Callback # callbacks; used in Trixi.jl + adaptive::Bool # whether the algorithm is adaptive; ignored + dtmax::Float64 # ignored + maxiters::Int # maximal number of time steps + tstops::Vector{Float64} # tstops from https://diffeq.sciml.ai/v6.8/basics/common_solver_opts/#Output-Control-1; ignored + verbose::Int + algo::Symbol + krylov_kwargs::Any +end + +function RKTableau(alg::RKLSSPIMEX332) +return RKLSSPIMEX332Tableau() +end + +function RKLSSPIMEX332Tableau() + + nstage = 3 + a = zeros(Float64, nstage, nstage) + a[2, 1] = 0.5 + a[3, 1] = 0.5 + a[3, 2] = 0.5 + + b = zeros(Float64, nstage) + b[1] = 1/3 + b[2] = 1/3 + b[3] = 1/3 + + c = zeros(Float64, nstage) + c[2] = 0.5 + c[3] = 1.0 + ah = zeros(Float64, nstage, nstage) + ah[1, 1] = 1/4 + ah[2, 2] = 1/4 + ah[3, 1] = 1/3 + ah[3, 2] = 1/3 + ah[3, 3] = 1/3 + + bh = zeros(Float64, nstage) + bh[1] = 1/3 + bh[2] = 1/3 + bh[3] = 1/3 + + ch = zeros(Float64, nstage) + ch[1] = 1/4 + ch[2] = 1/4 + ch[3] = 1.0 + return IMEXRKButcher(a, b, c, ah, bh, ch) +end + +function RKTableau(alg::RKLinearImplicitExplicitEuler) + return LinearImplicitExplicitEulerTableau() +end + +function LinearImplicitExplicitEulerTableau() + + nstage = 1 + a = zeros(Float64, nstage, nstage) + a[1, 1] = 1 + + b = zeros(Float64, nstage) + b[1] = 1 + + c = zeros(Float64, nstage) + c[1] = 1 + return DIRKButcher(a, b, c) +end + + +function SimpleLinearImplicitExplicitOptions(callback, tspan; maxiters=typemax(Int), verbose=0, krylov_algo=:gmres, krylov_kwargs=(;), kwargs...) + return SimpleLinearImplicitExplicitOptions{typeof(callback)}( + callback, false, Inf, maxiters, + [last(tspan)], + verbose, + krylov_algo, + krylov_kwargs, + ) +end + +mutable struct SimpleLinearImplicitExplicit{ + RealT<:Real,uType,Params,Sol,F,F1,F2,M,Alg<:SimpleLinearImplicitExplicitAlgorithm, + SimpleLinearImplicitExplicitOptions,RKTableau, +} <: AbstractTimeIntegrator + u::uType + du::uType + du_tmp::uType + lin_du_tmp::uType + lin_du_tmp1::uType + u_tmp::uType + stages::NTuple{M,uType} + ustages::NTuple{M,uType} + jstages::NTuple{M,uType} + res::uType + t::RealT + dt::RealT # current time step + dtcache::RealT # ignored + iter::Int # current number of time steps (iteration) + p::Params # will be the semidiscretization from Trixi.jl + sol::Sol # faked + f::F #TODO: that should be sum of f1 and f2 + f1::F1 # `rhs!` parabolic + f2::F2 # rhs! conservative + alg::Alg # SimpleImplicitAlgorithm + opts::SimpleLinearImplicitExplicitOptions + finalstep::Bool # added for convenience + RK::RKTableau +end + + +function Base.getproperty(integrator::SimpleLinearImplicitExplicit, field::Symbol) + if field === :stats + return (naccept=getfield(integrator, :iter),) + end + # general fallback + return getfield(integrator, field) +end + +function init( + ode::ODEProblem, alg::SimpleLinearImplicitExplicitAlgorithm{N}; + dt, callback::Union{CallbackSet,Nothing}=nothing, kwargs..., +) where {N} + u = copy(ode.u0) + du = zero(u) + res = zero(u) + u_tmp = similar(u) + stages = ntuple(_ -> similar(u), Val(N)) + ustages = ntuple(_ -> similar(u), Val(N)) + jstages = ntuple(_ -> similar(u), Val(N)) + t = first(ode.tspan) + iter = 0 + integrator = SimpleLinearImplicitExplicit( + u, du, copy(du),copy(du), copy(du), u_tmp,stages, ustages, jstages, res, t, dt, zero(dt), iter, ode.p, + (prob=ode,), ode.f.f1, ode.f.f1, ode.f.f2, alg, + SimpleLinearImplicitExplicitOptions( + callback, ode.tspan; + kwargs..., + ), false, RKTableau(alg)) + + # initialize callbacks + if callback isa CallbackSet + foreach(callback.continuous_callbacks) do cb + throw(ArgumentError("Continuous callbacks are unsupported with the implicit time integration methods.")) + end + foreach(callback.discrete_callbacks) do cb + cb.initialize(cb, integrator.u, integrator.t, integrator) + end + end + + return integrator +end + +# Fakes `solve`: https://diffeq.sciml.ai/v6.8/basics/overview/#Solving-the-Problems-1 +function solve( + ode::ODEProblem, alg::SimpleLinearImplicitExplicitAlgorithm; + dt, callback=nothing, kwargs..., +) + integrator = init(ode, alg, dt=dt, callback=callback; kwargs...) + + # Start actual solve + return solve!(integrator) +end + +function solve!(integrator::SimpleLinearImplicitExplicit) + @unpack prob = integrator.sol + + integrator.finalstep = false + + while !integrator.finalstep + step!(integrator) + end # "main loop" timer + + finalize_callbacks(integrator) + + return TimeIntegratorSolution( + (first(prob.tspan), integrator.t), + (prob.u0, integrator.u), + integrator.sol.prob, + ) +end + + +function step!(integrator::SimpleLinearImplicitExplicit) + @unpack prob = integrator.sol + @unpack alg = integrator + t_end = last(prob.tspan) + callbacks = integrator.opts.callback + + @assert !integrator.finalstep + if isnan(integrator.dt) + error("time step size `dt` is NaN") + end + + # if the next iteration would push the simulation beyond the end time, set dt accordingly + if integrator.t + integrator.dt > t_end || + isapprox(integrator.t + integrator.dt, t_end) + integrator.dt = t_end - integrator.t + terminate!(integrator) + end + + # one time step + integrator.u_tmp .= integrator.u + + stage!(integrator, alg) + + integrator.u .= integrator.u_tmp + + integrator.iter += 1 + integrator.t += integrator.dt + + begin + # handle callbacks + if callbacks isa CallbackSet + foreach(callbacks.discrete_callbacks) do cb + if cb.condition(integrator.u, integrator.t, integrator) + cb.affect!(integrator) + end + return nothing + end + end + end + + # respect maximum number of iterations + return if integrator.iter >= integrator.opts.maxiters && !integrator.finalstep + @warn "Interrupted. Larger maxiters is needed." + terminate!(integrator) + end +end + +function stage!(integrator, alg::RKLIMEX) + F!(du, u, p) = integrator.f1(du, u, p, integrator.t) ## parabolic + J = JacobianOperator(F!, integrator.du, integrator.u, integrator.p) + M = LMOperator(J, integrator.dt) + kc = KrylovConstructor(integrator.res) + workspace = krylov_workspace(:gmres, kc) + for stage in 1:stages(alg) + # Store the solution for each stage in stages + ## For a split Problem we need to compute rhs_conservative and rhs_parabolic + alg(integrator.res, integrator.u, integrator.dt, integrator.f1, integrator.f2, integrator.du, integrator.du_tmp, integrator.u_tmp, integrator.p, integrator.t, integrator.stages, integrator.ustages, integrator.jstages, stage, integrator.RK, M, integrator.lin_du_tmp, integrator.lin_du_tmp1, workspace) + + end +end + +# get a cache where the RHS can be stored +get_du(integrator::SimpleLinearImplicitExplicit) = integrator.du +get_tmp_cache(integrator::SimpleLinearImplicitExplicit) = (integrator.u_tmp,) + +# some algorithms from DiffEq like FSAL-ones need to be informed when a callback has modified u +u_modified!(integrator::SimpleLinearImplicitExplicit, ::Bool) = false + +# used by adaptive timestepping algorithms in DiffEq +function set_proposed_dt!(integrator::SimpleLinearImplicitExplicit, dt) + return integrator.dt = dt +end + +# Required e.g. for `glm_speed_callback` +function get_proposed_dt(integrator::SimpleLinearImplicitExplicit) + return integrator.dt +end + +# stop the time integration +function terminate!(integrator::SimpleLinearImplicitExplicit) + integrator.finalstep = true + return empty!(integrator.opts.tstops) +end + +# used for AMR +function Base.resize!(integrator::SimpleLinearImplicitExplicit, new_size) + resize!(integrator.u, new_size) + resize!(integrator.du, new_size) + return resize!(integrator.u_tmp, new_size) +end + diff --git a/libs/Implicit/src/skeleton.jl b/libs/Implicit/src/skeleton.jl new file mode 100644 index 0000000..1b7bb22 --- /dev/null +++ b/libs/Implicit/src/skeleton.jl @@ -0,0 +1,263 @@ +abstract type SimpleImplicitExplicitAlgorithm{N} end + +abstract type RKIMEX{N} <: SimpleImplicitExplicitAlgorithm{N} end + +struct RKImplicitExplicitEuler <: RKIMEX{1} end + +function (::RKImplicitExplicitEuler)(res, uₙ, Δt, f1!, f2!, du, du_tmp, u, p, t, stages, stage, RK) + if stage == 1 + # Stage 1: + ## f2 is the conservative part + ## f1 is the parabolic part + f2!(du, uₙ, p, t + RK.c[stage] * Δt ) + f1!(du_tmp, u, p, t + RK.c[stage] * Δt ) + return res .= u .- uₙ .- RK.a[stage, stage] * Δt .* du - RK.a[stage,stage] * Δt * du_tmp + else + @. u = uₙ + RK.b[1] * Δt * stages[1] + end + +end + +stages(::SimpleImplicitExplicitAlgorithm{N}) where {N} = N + +function nonlinear_problem(alg::SimpleImplicitExplicitAlgorithm, f2::F2) where {F2} + return (res, u, (uₙ, Δt, f1, du, du_tmp, p, t, stages, stage, RK)) -> alg(res, uₙ, Δt, f1, f2, du, du_tmp, u, p, t, stages, stage, RK) +end + +mutable struct SimpleImplicitExplicitOptions{Callback} + callback::Callback # callbacks; used in Trixi.jl + adaptive::Bool # whether the algorithm is adaptive; ignored + dtmax::Float64 # ignored + maxiters::Int # maximal number of time steps + tstops::Vector{Float64} # tstops from https://diffeq.sciml.ai/v6.8/basics/common_solver_opts/#Output-Control-1; ignored + verbose::Int + algo::Symbol + krylov_kwargs::Any +end + +function RKTableau(alg::RKImplicitExplicitEuler) + return ImplicitExplicitEulerTableau() +end + +function ImplicitExplicitEulerTableau() + + nstage = 1 + a = zeros(Float64, nstage, nstage) + a[1, 1] = 1 + + b = zeros(Float64, nstage) + b[1] = 1 + + c = zeros(Float64, nstage) + c[1] = 1 + return DIRKButcher(a, b, c) +end + + +function SimpleImplicitExplicitOptions(callback, tspan; maxiters=typemax(Int), verbose=0, krylov_algo=:gmres, krylov_kwargs=(;), kwargs...) + return SimpleImplicitExplicitOptions{typeof(callback)}( + callback, false, Inf, maxiters, + [last(tspan)], + verbose, + krylov_algo, + krylov_kwargs, + ) +end + +mutable struct SimpleImplicitExplicit{ + RealT<:Real,uType,Params,Sol,F,F1,F2,M,Alg<:SimpleImplicitExplicitAlgorithm, + SimpleImplicitExplicitOptions,RKTableau, +} <: AbstractTimeIntegrator + u::uType + du::uType + du_tmp::uType + u_tmp::uType + stages::NTuple{M,uType} + res::uType + t::RealT + dt::RealT # current time step + dtcache::RealT # ignored + iter::Int # current number of time steps (iteration) + p::Params # will be the semidiscretization from Trixi.jl + sol::Sol # faked + f::F #TODO: that should be sum of f1 and f2 + f1::F1 # `rhs!` parabolic + f2::F2 # rhs! conservative + alg::Alg # SimpleImplicitAlgorithm + opts::SimpleImplicitExplicitOptions + finalstep::Bool # added for convenience + RK::RKTableau +end + + +function Base.getproperty(integrator::SimpleImplicitExplicit, field::Symbol) + if field === :stats + return (naccept=getfield(integrator, :iter),) + end + # general fallback + return getfield(integrator, field) +end + +function init( + ode::ODEProblem, alg::SimpleImplicitExplicitAlgorithm{N}; + dt, callback::Union{CallbackSet,Nothing}=nothing, kwargs..., +) where {N} + u = copy(ode.u0) + du = zero(u) + res = zero(u) + u_tmp = similar(u) + stages = ntuple(_ -> similar(u), Val(N)) + t = first(ode.tspan) + iter = 0 + integrator = SimpleImplicitExplicit( + u, du, copy(du), u_tmp, stages, res, t, dt, zero(dt), iter, ode.p, + (prob=ode,), ode.f.f1, ode.f.f1, ode.f.f2, alg, + SimpleImplicitExplicitOptions( + callback, ode.tspan; + kwargs..., + ), false, RKTableau(alg)) + + # initialize callbacks + if callback isa CallbackSet + foreach(callback.continuous_callbacks) do cb + throw(ArgumentError("Continuous callbacks are unsupported with the implicit time integration methods.")) + end + foreach(callback.discrete_callbacks) do cb + cb.initialize(cb, integrator.u, integrator.t, integrator) + end + end + + return integrator +end + +# Fakes `solve`: https://diffeq.sciml.ai/v6.8/basics/overview/#Solving-the-Problems-1 +function solve( + ode::ODEProblem, alg::SimpleImplicitExplicitAlgorithm; + dt, callback=nothing, kwargs..., +) + integrator = init(ode, alg, dt=dt, callback=callback; kwargs...) + + # Start actual solve + return solve!(integrator) +end + +function solve!(integrator::SimpleImplicitExplicit) + @unpack prob = integrator.sol + + integrator.finalstep = false + + while !integrator.finalstep + step!(integrator) + end # "main loop" timer + + finalize_callbacks(integrator) + + return TimeIntegratorSolution( + (first(prob.tspan), integrator.t), + (prob.u0, integrator.u), + integrator.sol.prob, + ) +end + + +function step!(integrator::SimpleImplicitExplicit) + @unpack prob = integrator.sol + @unpack alg = integrator + t_end = last(prob.tspan) + callbacks = integrator.opts.callback + + @assert !integrator.finalstep + if isnan(integrator.dt) + error("time step size `dt` is NaN") + end + + # if the next iteration would push the simulation beyond the end time, set dt accordingly + if integrator.t + integrator.dt > t_end || + isapprox(integrator.t + integrator.dt, t_end) + integrator.dt = t_end - integrator.t + terminate!(integrator) + end + + # one time step + integrator.u_tmp .= integrator.u + + stage!(integrator, alg) + + integrator.u .= integrator.u_tmp + + integrator.iter += 1 + integrator.t += integrator.dt + + begin + # handle callbacks + if callbacks isa CallbackSet + foreach(callbacks.discrete_callbacks) do cb + if cb.condition(integrator.u, integrator.t, integrator) + cb.affect!(integrator) + end + return nothing + end + end + end + + # respect maximum number of iterations + return if integrator.iter >= integrator.opts.maxiters && !integrator.finalstep + @warn "Interrupted. Larger maxiters is needed." + terminate!(integrator) + end +end + + +function stage!(integrator, alg::RKIMEX) + for stage in 1:stages(alg) + F! = nonlinear_problem(alg, integrator.f2) + # TODO: Pass in `stages[1:(stage-1)]` or full tuple? + _, stats = Ariadne.newton_krylov!( + F!, integrator.u_tmp, (integrator.u, integrator.dt, integrator.f1, integrator.du, integrator.du_tmp, integrator.p, integrator.t, integrator.stages, stage, integrator.RK), integrator.res; + verbose=integrator.opts.verbose, krylov_kwargs=integrator.opts.krylov_kwargs, + algo=integrator.opts.algo, tol_abs=6.0e-6, + ) + @assert stats.solved + # Store the solution for each stage in stages + ## For a split Problem we need to compute rhs_conservative and rhs_parabolic + integrator.f2(integrator.du, integrator.u_tmp, integrator.p, integrator.t + integrator.RK.c[stage] * integrator.dt) + integrator.stages[stage] .= integrator.du + integrator.f1(integrator.du, integrator.u_tmp, integrator.p, integrator.t + integrator.RK.c[stage] * integrator.dt) + integrator.stages[stage] .+= integrator.du + if stage == stages(alg) + alg(integrator.res, integrator.u, integrator.dt, integrator.f1, integrator.f2, integrator.du, integrator.du_tmp, integrator.u_tmp, integrator.p, integrator.t, integrator.stages, stage + 1, integrator.RK) + end + + end +end + +# get a cache where the RHS can be stored +get_du(integrator::SimpleImplicitExplicit) = integrator.du +get_tmp_cache(integrator::SimpleImplicitExplicit) = (integrator.u_tmp,) + +# some algorithms from DiffEq like FSAL-ones need to be informed when a callback has modified u +u_modified!(integrator::SimpleImplicitExplicit, ::Bool) = false + +# used by adaptive timestepping algorithms in DiffEq +function set_proposed_dt!(integrator::SimpleImplicitExplicit, dt) + return integrator.dt = dt +end + +# Required e.g. for `glm_speed_callback` +function get_proposed_dt(integrator::SimpleImplicitExplicit) + return integrator.dt +end + +# stop the time integration +function terminate!(integrator::SimpleImplicitExplicit) + integrator.finalstep = true + return empty!(integrator.opts.tstops) +end + +# used for AMR +function Base.resize!(integrator::SimpleImplicitExplicit, new_size) + resize!(integrator.u, new_size) + resize!(integrator.du, new_size) + return resize!(integrator.u_tmp, new_size) +end + diff --git a/src/Ariadne.jl b/src/Ariadne.jl index 2be23dc..39217fe 100644 --- a/src/Ariadne.jl +++ b/src/Ariadne.jl @@ -11,51 +11,130 @@ using Enzyme ## import LinearAlgebra: mul! -function maybe_duplicated(x, ::Val{N} = Val(1)) where {N} - # TODO cache? +function init_cache(x) if !Enzyme.Compiler.guaranteed_const(typeof(x)) - if N == 1 - return Duplicated(x, Enzyme.make_zero(x)) - else - return BatchDuplicated(x, ntuple(_ -> Enzyme.make_zero(x), Val(N))) - end + Enzyme.make_zero(x) else + return nothing + end +end + +function maybe_duplicated(x::T, x′::Union{Nothing, T}) where {T} + if x′ === nothing return Const(x) + else + Enzyme.remake_zero!(x′) + return Duplicated(x, x′) end end -# TODO: JacobianOperator with thunk +abstract type AbstractJacobianOperator end + """ JacobianOperator Efficient implementation of `J(f,x,p) * v` and `v * J(f, x,p)'` """ -struct JacobianOperator{F, A, P} +struct JacobianOperator{F, A, P} <: AbstractJacobianOperator f::F # F!(res, u, p) + f′::Union{Nothing, F} # cache res::A u::A p::P + p′::Union{Nothing, P} # cache function JacobianOperator(f::F, res, u, p) where {F} - return new{F, typeof(u), typeof(p)}(f, res, u, p) + f′ = init_cache(f) + p′ = init_cache(p) + return new{F, typeof(u), typeof(p)}(f, f′, res, u, p, p′) end end +batch_size(::JacobianOperator) = 1 + Base.size(J::JacobianOperator) = (length(J.res), length(J.u)) Base.eltype(J::JacobianOperator) = eltype(J.u) Base.length(J::JacobianOperator) = prod(size(J)) -function mul!(out::AbstractVector, J::JacobianOperator, v::AbstractVector) +function mul!(out, J::JacobianOperator, v) autodiff( Forward, - maybe_duplicated(J.f), Const, + maybe_duplicated(J.f, J.f′), Const, Duplicated(J.res, reshape(out, size(J.res))), Duplicated(J.u, reshape(v, size(J.u))), - maybe_duplicated(J.p) + maybe_duplicated(J.p, J.p′) ) return nothing end +LinearAlgebra.adjoint(J::JacobianOperator) = Adjoint(J) +LinearAlgebra.transpose(J::JacobianOperator) = Transpose(J) + +# Jᵀ(y, u) = ForwardDiff.gradient!(y, x -> dot(F(x), u), xk) +# or just reverse mode + +function mul!(out, J′::Union{Adjoint{<:Any, <:JacobianOperator}, Transpose{<:Any, <:JacobianOperator}}, v) + J = parent(J′) + # TODO: provide cache for `copy(v)` + # Enzyme zeros input derivatives and that confuses the solvers. + # If `out` is non-zero we might get spurious gradients + fill!(out, 0) + autodiff( + Reverse, + maybe_duplicated(J.f, J.f′), Const, + Duplicated(J.res, reshape(copy(v), size(J.res))), + Duplicated(J.u, reshape(out, size(J.u))), + maybe_duplicated(J.p, J.p′) + ) + return nothing +end + + +function init_cache(x, ::Val{N}) where {N} + if !Enzyme.Compiler.guaranteed_const(typeof(x)) + return ntuple(_ -> Enzyme.make_zero(x), Val(N)) + else + return nothing + end +end + +function maybe_duplicated(x::T, x′::Union{Nothing, NTuple{N, T}}, ::Val{N}) where {T, N} + if x′ === nothing + return Const(x) + else + Enzyme.remake_zero!(x′) + return BatchDuplicated(x, x′) + end +end + +""" + BatchedJacobianOperator{N} + + +""" +struct BatchedJacobianOperator{N, F, A, P} <: AbstractJacobianOperator + f::F # F!(res, u, p) + f′::Union{Nothing, NTuple{N, F}} # cache + res::A + u::A + p::P + p′::Union{Nothing, NTuple{N, P}} # cache + function BatchedJacobianOperator{N}(f::F, res, u, p) where {F, N} + f′ = init_cache(f, Val(N)) + p′ = init_cache(p, Val(N)) + return new{N, F, typeof(u), typeof(p)}(f, f′, res, u, p, p′) + end +end + +batch_size(::BatchedJacobianOperator{N}) where {N} = N + +Base.size(J::BatchedJacobianOperator) = (length(J.res), length(J.u)) +Base.eltype(J::BatchedJacobianOperator) = eltype(J.u) +Base.length(J::BatchedJacobianOperator) = prod(size(J)) + +LinearAlgebra.adjoint(J::BatchedJacobianOperator) = Adjoint(J) +LinearAlgebra.transpose(J::BatchedJacobianOperator) = Transpose(J) + if VERSION >= v"1.11.0" function tuple_of_vectors(M::Matrix{T}, shape) where {T} @@ -66,49 +145,23 @@ if VERSION >= v"1.11.0" end end - function mul!(Out::AbstractMatrix, J::JacobianOperator, V::AbstractMatrix) + function mul!(Out, J::BatchedJacobianOperator{N}, V) where {N} @assert size(Out, 2) == size(V, 2) out = tuple_of_vectors(Out, size(J.res)) v = tuple_of_vectors(V, size(J.u)) - N = length(out) + @assert N == length(out) autodiff( Forward, - maybe_duplicated(J.f, Val(N)), Const, + maybe_duplicated(J.f, J.f′, Val(N)), Const, BatchDuplicated(J.res, out), BatchDuplicated(J.u, v), - maybe_duplicated(J.p, Val(N)) + maybe_duplicated(J.p, J.p′, Val(N)) ) return nothing end -end # VERSION >= v"1.11.0" - -LinearAlgebra.adjoint(J::JacobianOperator) = Adjoint(J) -LinearAlgebra.transpose(J::JacobianOperator) = Transpose(J) - -# Jᵀ(y, u) = ForwardDiff.gradient!(y, x -> dot(F(x), u), xk) -# or just reverse mode - -function mul!(out::AbstractVector, J′::Union{Adjoint{<:Any, <:JacobianOperator}, Transpose{<:Any, <:JacobianOperator}}, v::AbstractVector) - J = parent(J′) - # TODO: provide cache for `copy(v)` - # Enzyme zeros input derivatives and that confuses the solvers. - # If `out` is non-zero we might get spurious gradients - fill!(out, 0) - autodiff( - Reverse, - maybe_duplicated(J.f), Const, - Duplicated(J.res, reshape(copy(v), size(J.res))), - Duplicated(J.u, reshape(out, size(J.u))), - maybe_duplicated(J.p) - ) - return nothing -end - -if VERSION >= v"1.11.0" - - function mul!(Out::AbstractMatrix, J′::Union{Adjoint{<:Any, <:JacobianOperator}, Transpose{<:Any, <:JacobianOperator}}, V::AbstractMatrix) + function mul!(Out, J′::Union{Adjoint{<:Any, <:BatchedJacobianOperator{N}}, Transpose{<:Any, <:BatchedJacobianOperator{N}}}, V) where {N} J = parent(J′) @assert size(Out, 2) == size(V, 2) @@ -122,22 +175,20 @@ if VERSION >= v"1.11.0" out = tuple_of_vectors(Out, size(J.u)) v = tuple_of_vectors(V, size(J.res)) - N = length(out) + @assert N == length(out) - # TODO: BatchDuplicated for J.f autodiff( Reverse, - maybe_duplicated(J.f, Val(N)), Const, + maybe_duplicated(J.f, J.f′, Val(N)), Const, BatchDuplicated(J.res, v), BatchDuplicated(J.u, out), - maybe_duplicated(J.p, Val(N)) + maybe_duplicated(J.p, J.p′, Val(N)) ) return nothing end - end # VERSION >= v"1.11.0" -function Base.collect(JOp::Union{Adjoint{<:Any, <:JacobianOperator}, Transpose{<:Any, <:JacobianOperator}, JacobianOperator}) +function Base.collect(JOp::Union{Adjoint{<:Any, <:AbstractJacobianOperator}, Transpose{<:Any, <:AbstractJacobianOperator}, AbstractJacobianOperator}) N, M = size(JOp) if JOp isa JacobianOperator v = zero(JOp.u)