Abstract

We present a one-way dissection formulation of high-order compact scheme for the solution of 2D Poisson equation. One-way dissection is a type of matrix reordering, divide and conquers procedure. Efficient and concise compact schemes of 4th and 6th orders are derived using the truncation errors of the Taylors’ series expansion of the governing equation. The system is split into sub-domains and each sub-domain is treated separately. Two test problems are solved to show the fourth order performance of the scheme. The direct method is used to achieve a quick solution to the problems.

Key words: Poisson equation, one-way dissection, high-order compact scheme, sparse matrix, direct method.