update packages to LinearSolve@v3

[oscardssmith]

fixes #231. Requires SciML/LinearSolve.jl#803 for tests to pass.

[oscardssmith]

@termi-official want me to include MTKv10 in this PR? it seems to work fine from the tests locally at least.

[termi-official]

@termi-official want me to include MTKv10 in this PR? it seems to work fine from the tests locally at least.

I will do this separately with proper test coverage.

[termi-official]

I think the test for sol_prec.resid < sol_unprec.resid should be simply removed here. I do this is not a guaranteed condition and it just happens in this test case that the preconditioned residual is smaller than the unpreconditioned one.

[codecov]

Codecov Report

❌ Patch coverage is 66.66667% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 61.26%. Comparing base (b26e81a) to head (5775f9b).

Files with missing lines	Patch %	Lines
src/solver/nonlinear/newton_raphson.jl	50.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #233      +/-   ##
==========================================
- Coverage   62.22%   61.26%   -0.97%     
==========================================
  Files          77       77              
  Lines        6367     6364       -3     
==========================================
- Hits         3962     3899      -63     
- Misses       2405     2465      +60     

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[oscardssmith]

@termi-official are we really testing the time the linsolve takes?

[termi-official]

Yes. There should be at least an order difference between those.