Numerical Solution of Poisson's Equation with Arbitrarily Shaped Boundaries Using a Domain Decomposition and Overlapping Technique
Abstract
A directsolution scheme for numerically solving the 3dimensional Poisson's problem with arbitrarily shaped boundaries ∇ · (λ∇φ) = S on Ω, C _{1}φ + C _{2}n · (λ∇φ) = C _{3} on ∂Ω, has been developed by using a boundaryfitted 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 largescale engineering problems.
 Publication:

Journal of Computational Physics
 Pub Date:
 December 1986
 DOI:
 10.1016/00219991(86)902627
 Bibcode:
 1986JCoPh..67..263M