A Neural-preconditioned Poisson Solver for Mixed Dirichlet and Neumann Boundary Conditions

arXiv:2310.00177v5 Announce Type: replace-cross
Abstract: We introduce a neural-preconditioned iterative solver for Poisson equations with mixed boundary conditions. Typical Poisson discretizations yield large, ill-conditioned linear systems. Iterative solvers can be effective for these problems, but only when equipped with powerful preconditioners. Unfortunately, effective preconditioners like multigrid require costly setup phases that must be re-executed every time domain shapes or boundary conditions change, forming a severe bottleneck for problems with evolving boundaries. In contrast, we present a neural preconditioner trained to …

abstract arxiv cs.lg cs.na iterative linear math.na mixed replace setup solver systems type