ABSTRACT
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.
The author would like to acknowledge financial support from the Thailand Research Fund.