Numerical solution of poisson's equation with arbitrarily shaped boundaries using a domain decomposition and overlapping technique

Abstract

A direct-solution scheme for numerically solving the 3-dimensional Poisson's problem with arbitrarily shaped boundaries ∇ · (λ∇φ) = S on Ω, C 1φ + C 2n · (λ∇φ) = C 3 on ∂Ω, has been developed by using a boundary-fitted coordinate transformation. The scheme also used the technique of decomposing the closed domain Ω into several hexahedron subdomains and then overlapping neighboring hexahedrons to deal with complicated geometries. A large system of linear equations derived from discretizing the Poisson's equation was solved by using a biconjugate gradient method with incomplete LU factorization of the nonsymmetric coefficient matrix as preconditioning. The convergence behavior of the different domain decompositions was demonstrated for a numerical experiment. Application to the electrostatic field problem in the electron gun of a color picture tube confirms that the present numerical scheme should provide an efficient and convenient tool for solving many important large-scale engineering problems.