User defined RHS Splitting for IMEX

[MarcoArtiano]

The following PR implements a way for the user to define a splitting for the RHS by calling SemidiscretizationHyperbolicSplit and defining two solver (implicit and explicit). The semidiscretize object returns a SplitODEProblem, which can be solved via an IMEX method.

See: https://docs.sciml.ai/OrdinaryDiffEq/stable/imex/IMEXBDF/, for a list of some semi-implicit solvers.

See: IMEX example for a test case example.

Features:

• Define explicit and implicit solvers (only flux differencing, to avoid incorrect definition of the rhs of the implicit or explicit part due to analytical flux being used in the weak form)
• Define boundary conditions for the implicit and explicit part
• Define source terms for the implicit and explicit part
• The splitting has to be defined as $$y_t = f_1(y) + f_2(y)$$

[github-actions]

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Created with ❤️ by the Trixi.jl community.

[codecov]

Codecov Report

❌ Patch coverage is 99.35484% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 97.13%. Comparing base (ccb7fe5) to head (cbf46f8).

Files with missing lines	Patch %	Lines
src/semidiscretization/semidiscretization_split.jl	98.55%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2518      +/-   ##
==========================================
+ Coverage   97.12%   97.13%   +0.01%     
==========================================
  Files         627      629       +2     
  Lines       48610    48765     +155     
==========================================
+ Hits        47212    47366     +154     
- Misses       1398     1399       +1     

Flag	Coverage Δ
unittests	97.13% <99.35%> (+0.01%)	⬆️

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[DanielDoehring]

@MarcoArtiano you can ping me for review when you feel this is ready - I have recently more or less familiarized myself with the splitfunction/splitproblem business

[MarcoArtiano]

@DanielDoehring this is ready for a review. I've changed the splitting to have something a bit more meaningful.

[MarcoArtiano]

@ranocha this should be ready to be merged.

[ranocha]

Thanks! I just have a few comments.

[ranocha]

The docstring and the implementation do not match for the solvers.

[ranocha]

@MarcoArtiano This comment is still open

[MarcoArtiano]

Sorry, I have forgotten to push, now it is updated.

[ranocha]

Thanks

[DanielDoehring]

I observe https://github.com/trixi-framework/Trixi.jl/actions/runs/25846689367/job/75943597855#step:7:12671 which is similar to

Trixi.jl/test/test_trixi.jl

Lines 18 to 19 in dfdb226

	r"┌ Warning: The call to compilecache failed to create a usable precompiled cache file for OrdinaryDiffEqSDIRK \[2d112036-d095-4a1e-ab9a-08536f3ecdbf\]\n│ exception = Required dependency OrdinaryDiffEqDifferentiation \[4302a76b-040a-498a-8c04-15b101fed76b\] failed to load from a cache file.\n└ @ Base loading.jl:.+\n",
	r"\e\[33m\e\[1m┌ \e\[22m\e\[39m\e\[33m\e\[1mWarning: \e\[22m\e\[39mModule OrdinaryDiffEqSDIRK with build ID .+ is missing from the cache.\n\e\[33m\e\[1m│ \e\[22m\e\[39mThis may mean OrdinaryDiffEqSDIRK \[2d112036-d095-4a1e-ab9a-08536f3ecdbf\] does not support precompilation but is imported by a module that does.\n\e\[33m\e\[1m└ \e\[22m\e\[39m\e\[90m@ Base loading.jl:.+\e\[39m\n",

[MarcoArtiano]

I observe https://github.com/trixi-framework/Trixi.jl/actions/runs/25846689367/job/75943597855#step:7:12671 which is similar to

Trixi.jl/test/test_trixi.jl

Lines 18 to 19 in dfdb226

	r"┌ Warning: The call to compilecache failed to create a usable precompiled cache file for OrdinaryDiffEqSDIRK \[2d112036-d095-4a1e-ab9a-08536f3ecdbf\]\n│ exception = Required dependency OrdinaryDiffEqDifferentiation \[4302a76b-040a-498a-8c04-15b101fed76b\] failed to load from a cache file.\n└ @ Base loading.jl:.+\n",
	r"\e\[33m\e\[1m┌ \e\[22m\e\[39m\e\[33m\e\[1mWarning: \e\[22m\e\[39mModule OrdinaryDiffEqSDIRK with build ID .+ is missing from the cache.\n\e\[33m\e\[1m│ \e\[22m\e\[39mThis may mean OrdinaryDiffEqSDIRK \[2d112036-d095-4a1e-ab9a-08536f3ecdbf\] does not support precompilation but is imported by a module that does.\n\e\[33m\e\[1m└ \e\[22m\e\[39m\e\[90m@ Base loading.jl:.+\e\[39m\n",

Do you know the cause of that?

It seems that simply adding the similar warning for OrdinaryDiffEqBDF should solve the issue.

Another alternative would be to use Ariadne.jl, which is more performant, but still in its early development phase. @vchuravy

[ranocha]

I added a corresponding ignore setting in #3010 (still to be reviewed).