Allow updating coefficients and reuse same solver instances. (Draft)

[julianlitz]

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[julianlitz]

@EmilyBourne

It is possible to add such update Function.

Then you can keep using the same instance and avoid costly memory allocations.

I made this quick proof of concept with Claude.

Just let me know if we need such functionality or if you are fine with creating a new solver instance.
Depends how often you need to create a new instance if this refactoring is worth the effort.

[julianlitz]

Getting Mumps and the CSR solver to work correctly will be a pain 😂

We can also just ignore those and do a full rebuild just for the smoothers and direct solver.

Then at least we avoid the level allocations.