The Fast 3D Immersed Interface Method for Poisson Equations on Irregular Domains

Abstract

In this paper, Based on the IIM proposed by LeVeque and Li, [SIAM J. Numer. Anal., 31(1994), pp. 10191044] we will investigate and analyze some applications of the fast 3D solver, we developed embedding techniques to solve interior as well as exterior Poisson equations on complicated regions with Dirichlet or Neumann boundary conditions. The number of iterations in solving the Schur complement system appears to be independent of both the jump in the coefficient and the mesh size.