Solving a PDE on a submesh

2 months 1 week ago - 2 months 1 week ago #2476 by JSR
I'm trying to solve a PDE system on a 2D domain. The PDE has the form
\[\partial_tb + \Delta p=\lambda b\]
where p is a function that satisfies different equations on different subdomains:
\[\nabla\cdot\frac{1}{b}\nabla p = f(b)\quad\text{ when }b>b_p\\ p=0\qquad \text{ when }b\leq b_p\]

At each time-step I want to find the region(s) where b>b_p (b_p is a constant, but the region defined by this threshold will change over time), and then solve the PDE for p on that subdomain/submesh.

Is there a way to do this kind of thing (i.e. solving a PDE on a subset of the domain) using NGSolve?

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2 months 1 week ago #2478 by christopher
Hi
have you had a look at the NGSolve extension ngsxfem?
github.com/ngsxfem/ngsxfem
I think this is what you are looking for.

Best
Christopher

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2 months 1 week ago #2481 by JSR
That looks like it may do exactly what I want.
Thanks!

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