三维泊松方程的七点差分格式

The Seven-point Difference Scheme for the Three-dimensional Poisson's Equation

泊松方程在地球物理中的应用非常广泛,随着三维勘探的展开,三维泊松方程的快速、精确求解变得越来越重要。本文用有限差分方法推导出长方体域的三维泊松方程的七点差分格式,及其边界条件的差分格式,并对满足第一类边界条件的七点差分格式进行求解,详细推导了七点差分格式的求解过程。

Poisson＇s equation in the geophysics is widely used. With the starting of the three-dimensional exploration, the fast and accurate solution of the three-dimensional Poisson＇s equation has become more and more important. In this paper, I derive a seven-point difference scheme for the three-dimensional rectangular domain Poisson＇s equation and its boundary conditions by the finite difference method, then solve it, which meets the first boundary condition, and give a detailed derivation process of the seven-point difference scheme.