I would like to solve two types of simple 2D problems, namely the stationary heat equation on an L shaped geometry like this:
And also compute the magnetostactic field in an air gap of the following geometry:
Since it wouldn’t be smart to reinvent the wheel, I searched for an open-source library that could handle such problems. At far as I could tell, neither in Python, Octave, Scilab or R there is a Finite-Difference (FD) library that could handle this type of geometries, which is not rectangular but should nonetheless fit on a rectangular grid (if I remember correctly from reading from “Heat Transfer” from Incropera, internal and external nodes can be handled by FD)
This lack of availability strikes me as odd; Python, Octave, Scilab and R all of them have built-in libraries for solution of ODEs, but why not FD for PDEs? Was it concluded that focusing on Finite-Element (FE) would be enough/better? I would like to stay with FD for two reasons: simplicity and I would like in the future to solve other types of PDEs, which may not be available on a FE solver.
Would it make sense to think of developing such a library? Are the limitations of FD (to simple geometries) not worth the effort?
Many thanks in advance!