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Add Trixi example (#7)
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‎docs/LocalPreferences.toml‎

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[Trixi]
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loop_vectorization = false
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backend = "static"
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‎docs/Project.toml‎

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[deps]
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Ariadne = "0be81120-40bf-4f8b-adf0-26103efb66f1"
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CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
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DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
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Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
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DocumenterCitations = "daee34ce-89f3-4625-b898-19384cb65244"
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KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
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Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
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KrylovPreconditioners = "45d422c2-293f-44ce-8315-2cb988662dec"
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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Literate = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
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Ariadne = "0be81120-40bf-4f8b-adf0-26103efb66f1"
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OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
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OrdinaryDiffEqLowStorageRK = "b0944070-b475-4768-8dec-fb6eb410534d"
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OrdinaryDiffEqSDIRK = "2d112036-d095-4a1e-ab9a-08536f3ecdbf"
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OrdinaryDiffEqSSPRK = "669c94d9-1f4b-4b64-b377-1aa079aa2388"
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PlutoStaticHTML = "359b1769-a58e-495b-9770-312e911026ad"
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SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
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SummationByPartsOperators = "9f78cca6-572e-554e-b819-917d2f1cf240"
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Theseus = "7f538e44-2768-4ef2-af90-2110c0378286"
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Trixi = "a7f1ee26-1774-49b1-8366-f1abc58fbfcb"
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[sources]
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Ariadne = {path = ".."}
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Theseus = {path = "../libs/Theseus"}
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[compat]
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Trixi = "0.13.1"

‎docs/make.jl‎

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"Implicit -- Heat 1D" => "heat_1D",
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"Implicit -- Heat 1D DG" => "heat_1D_DG",
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"Implicit -- Heat 2D" => "heat_2D",
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"Trixi" => "trixi",
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]
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for (_, name) in examples

‎docs/src/refs.bib‎

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urldate = {2024-10-21},
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language = {en}
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}
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@ARTICLE{Hosea1996-xv,
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title = {Analysis and implementation of {TR}-{BDF2}},
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author = {Hosea, M E and Shampine, L F},
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journaltitle = {Applied numerical mathematics: transactions of IMACS},
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publisher = {Elsevier BV},
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volume = {20},
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issue = {1-2},
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pages = {21--37},
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date = {1996-02-01},
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doi = {10.1016/0168-9274(95)00115-8},
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issn = {0168-9274,1873-5460},
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urldate = {2025-03-04},
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language = {en}
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}
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@ARTICLE{Bank1985-gh,
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title = {Transient simulation of silicon devices and circuits},
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author = {Bank, R E and Coughran, W M and Fichtner, W and Grosse, E H
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and Rose, D J and Smith, R K},
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journaltitle = {IEEE transactions on electron devices},
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publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
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volume = {32},
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issue = {10},
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pages = {1992--2007},
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date = {1985-10},
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doi = {10.1109/t-ed.1985.22232},
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issn = {0018-9383,1557-9646},
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urldate = {2025-05-27},
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language = {en}
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}
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@ARTICLE{Bonaventura2021-za,
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title = {The {TR}-{BDF2} method for second order problems in structural
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mechanics},
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author = {Bonaventura, Luca and Mármol, Macarena Gómez},
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journaltitle = {Computers \& mathematics with applications (Oxford, England:
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1987)},
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publisher = {Elsevier BV},
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volume = {92},
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pages = {13--26},
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date = {2021-06-15},
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doi = {10.1016/j.camwa.2021.03.037},
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issn = {0898-1221,1873-7668},
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urldate = {2025-05-27},
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language = {en}
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}

‎examples/LocalPreferences.toml‎

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[Trixi]
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loop_vectorization = false
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backend = "static"

‎examples/Project.toml‎

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[deps]
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Ariadne = "0be81120-40bf-4f8b-adf0-26103efb66f1"
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CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
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ComponentArrays = "b0b7db55-cfe3-40fc-9ded-d10e2dbeff66"
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DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
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Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
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Theseus = "7f538e44-2768-4ef2-af90-2110c0378286"
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KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
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Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
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KrylovPreconditioners = "45d422c2-293f-44ce-8315-2cb988662dec"
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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Ariadne = "0be81120-40bf-4f8b-adf0-26103efb66f1"
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Observables = "510215fc-4207-5dde-b226-833fc4488ee2"
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OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
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OrdinaryDiffEqLowStorageRK = "b0944070-b475-4768-8dec-fb6eb410534d"
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OrdinaryDiffEqSDIRK = "2d112036-d095-4a1e-ab9a-08536f3ecdbf"
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OrdinaryDiffEqSSPRK = "669c94d9-1f4b-4b64-b377-1aa079aa2388"
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SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
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SummationByPartsOperators = "9f78cca6-572e-554e-b819-917d2f1cf240"
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Trixi = "a7f1ee26-1774-49b1-8366-f1abc58fbfcb"
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[sources]
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Ariadne = {path = ".."}
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Theseus = {path = "../libs/Theseus"}
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[compat]
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julia = "1.10"
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Trixi = "0.13.1"

‎examples/implicit.jl‎

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# # [Implicit schemes](@id implicit_schemes)
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using Ariadne
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using Ariadne
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# ## Implicit Euler
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function G_Euler!(res, uₙ, Δt, f!, du, u, p, t)

‎examples/trixi.jl‎

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# # Using the an implicit solver based on Ariadne with Trixi.jl
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using Trixi
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using Theseus
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using CairoMakie
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using LinearAlgebra
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import Ariadne: JacobianOperator
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# Notes:
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# Must disable both Polyester and LoopVectorization for Enzyme to be able to differentiate Trixi.jl
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# Using https://github.com/trixi-framework/Trixi.jl/pull/2295
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#
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# LocalPreferences.jl
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# ```toml
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# [Trixi]
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# loop_vectorization = false
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# backend = "static"
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# ```
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@assert Trixi._PREFERENCE_THREADING !== :polyester
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@assert !Trixi._PREFERENCE_LOOPVECTORIZATION
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# ## Load Trixi Example
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trixi_include(@__MODULE__, joinpath(examples_dir(), "tree_2d_dgsem", "elixir_advection_basic.jl"), sol = nothing);
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u = copy(ode.u0)
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du = zero(ode.u0)
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res = zero(ode.u0)
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F! = Theseus.nonlinear_problem(Theseus.ImplicitEuler(), ode.f)
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J = JacobianOperator(F!, res, u, (ode.u0, 1.0, du, ode.p, 0.0, (), 1))
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out = zero(u)
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v = zero(u)
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## precompile
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mul!(u, J, v)
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F!(res, u, (ode.u0, 1.0, du, ode.p, 0.0, (), 1))
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@time mul!(u, J, v)
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@time F!(res, u, (ode.u0, 1.0, du, ode.p, 0.0, (), 1))
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# Cost of time(mul!) ≈ 2 * time(F!)
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# ### Solve using ODE interface
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sol_trbdf2 = solve(
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ode, Theseus.TRBDF2();
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dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
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ode_default_options()..., callback = callbacks,
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## verbose=1,
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krylov_algo = :gmres,
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## krylov_kwargs=(;verbose=1)
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);
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# #### Plot the solution
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# We have to manually convert the sol since Theseus has it's own leightweight solution type.
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plot(Trixi.PlotData2DTriangulated(sol_trbdf2.u[end], sol_trbdf2.prob.p))
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# ### Solve using OrdinaryDiffEqSDIRKSDIRK
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import OrdinaryDiffEqSDIRK
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import DifferentiationInterface: AutoFiniteDiff
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sol_sdrik = solve(
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ode, OrdinaryDiffEqSDIRK.TRBDF2(autodiff = AutoFiniteDiff());
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dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
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ode_default_options()..., callback = callbacks,
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adaptive = false
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);
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# #### Plot the solution
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plot(Trixi.PlotData2DTriangulated(sol_sdrik.u[end], sol_sdrik.prob.p))
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# ## Increase CFL numbers
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trixi_include(@__MODULE__, joinpath(examples_dir(), "tree_2d_dgsem", "elixir_advection_basic.jl"), cfl = 10, sol = nothing);
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sol = solve(
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ode, Theseus.ImplicitEuler();
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dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback
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ode_default_options()..., callback = callbacks,
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## verbose=1,
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krylov_algo = :gmres,
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## krylov_kwargs=(;verbose=1)
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);
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@show callbacks.discrete_callbacks[4]
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# ### Plot the solution
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plot(Trixi.PlotData2DTriangulated(sol.u[end], sol.prob.p))

‎libs/Theseus/Project.toml‎

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name = "Theseus"
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uuid = "7f538e44-2768-4ef2-af90-2110c0378286"
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authors = ["Valentin Churavy <[email protected]>"]
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version = "0.1.0"
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[deps]
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DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
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Ariadne = "0be81120-40bf-4f8b-adf0-26103efb66f1"
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SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
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UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
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[sources]
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Ariadne = {path = "../.."}
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[compat]
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DiffEqBase = "6.174.0"
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Ariadne = "0.1.0"
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SciMLBase = "2.91.0"
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UnPack = "1.0.2"

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