Two Cartesian grid methods for solving the Poisson problem in an arbitrary domain

摘要

Two methods for solving the Poisson problem on an automatically generated Cartesian grid are proposed. The first method is a combination of the finite-element method and the boundary-element method. The second method is a combination of the finite-difference method and the method of fundamental solutions. Both methods split the problem into an inhomogeneous differential equation with homogeneous boundary conditions and a homogeneous differential equation with inhomogeneous boundary conditions. Numerical tests of the two methods using a sample problem reveal that they yield satisfactory results.