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Evening project: implementing a solver in GNU Octave for Laplace's equation, to have a simple libre system for FEM:ing electrostatics. Using 1.7x1.7x1.7 mm elements in a 150x150x150 mm domain results in a 516600x516600 sparse equation system (nnz=3553440), which UMFPACK quite happily solves in a few minutes
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Forgot a picture. This is a slice showing voltages in the XZ plane https://social.umeahackerspace.se/attachment/456969
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Trying to go down to 1.0 mm elements, but alas:
warning: warning -3, at line 683 in file ../Supernodal/cholmod_super_symbolic.c: problem too large
I probably have to switch to something like a biconjugate solver
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Turns out Octave has an implementation of the biconjugate gradient stabilized method (BiCGSTAB) which is much much faster and memory efficient than good old A\rhs or LU factorization