Abstract
Resolving the difficulty of T-junctions in Octree grids, Losasso et al. [9] introduced an ingenious Poisson solver with rectangular domains and Neumann boundary conditions. Its numerical solution was empirically observed [9] to be second order convergent and its numerical gradient was rigorously proved [8] to be one and a half order convergent, which is the so-called super-convergence.This article is devoted to extending the Poisson solver and its supporting proof from rectangular to irregular domains. The generalized Whitney decomposition [12] efficiently generates octree grids for irregular domains imposing the finest resolution near the boundary of domain. Combined with the Heaviside treatment [17,4], the Poisson solver is extended to irregular domains and a novel and rigorous analysis shows that the aforementioned super-convergence still holds true.
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