Spatially varying heat transfer coefficient and heat source

[nikoscham]

Spatially varying heat transfer coefficient and heat source at the heatConductionScript. Evaluate $k(x,y)$ and $Q(x,y)$ at the Gauss points.

[Ed6003]

Hi @nikoscham,

I know you self-assigned this and worked on it in May, I've started having a go at
it as well, keeping the naming from your linked branch. Before I go further, would
you rather I rebased onto your branch, or is it easier if I work from main and you
cherry-pick anything useful?

One thing I wasn't sure about, I was looking at your branch: do the coefficients need passing to solveAsync() as
well as solve()?

I was also going to add regression tests for the spatially varying coefficients even if the original tests are backwards compatible if coefficients aren't provided, including one checking they reach the assembler in solveAsync(). The existing tests
pass, but nothing covers this feature specifically, let me know if that'd be useful.

[nikoscham]

Hi @Ed6003 !

Thanks for picking it up! I have now merged the latest main into the feature/spatially-varying-coefficients branch. I propose to work on the specific branch and open PR with your changes there.

Yes, spatial coefficient functions should apply to solveAsync() too. I checked the current code and solveAsync() does not yet forward this.coefficientFunctions to assembleHeatConductionMat, while solve() does, so that is a gap.

Dedicated regression tests for varying thermalConductivity and `heatSource would be very useful. You can go on with that.

[Ed6003]

Opened #91 as a draft.

solveAsync() now forwards coefficientFunctions too, with a regression test to confirm it. I also mutation-tested the new regression tests locally to make sure they fail when they should. Also tested against the website per CONTRIBUTING.md, ran the working tree through the worker and WebGPU tutorials, and jacobi-gpu/solveAsync completes fine on both.

One small thing though npm test didn't work for me on Node v24.14.1, but node --test and everything passed.

[nikoscham]

Thanks a lot for your contribution @Ed6003. I will check the issue with npm test. I like your idea about closed-form solutions. Maybe we should find similar closed-form tests for all the solvers. I will do some more checks and then I will merge the changes with the main branch.

[Ed6003]

Thanks for the feedback @nikoscham. I agree both pinned regression tests and closed-form/analytical tests are useful. If you would like to add more, I'm wondering whether it's worth a separate folder for the analytical ones, similar to how tests/unit sits alongside tests/regression, maybe something like tests/verification.

They do act like regression tests in that they'll fail if something breaks, but I think they're really answering a similar but different question: is this still mathematically correct, rather than has this changed. Can keep together and just describe in REGRESSION.md or separate, no strong preference from me.

EulerBernoulliBeam seems worth doing too, and should be relatively inexpensive.
Possibly a closed-form solution can be done on generalFormPDEScript since jacobiSolver unit test doesn't touch the PDE.
I'm not too sure about creepingFlowScript and frontPropagationScript, these seem trickier.