关键词: 边界积分方程；区域积分；规则网格；边界点法；Poisson方程

Abstract:

The use of Cartesian grids is proposed to treat domain integrals encountered in the numerical solution of Poisson equations with boundary integral equations. Traditionally, domain integrals are treated by using internal cells, which makes the algorithm stable and accurate but takes much human labor. By introducing Cartesian grids, the time for data preparation is greatly reduced while keeping all merits of using internal cells. This is because cells have nothing to do with the handling of boundary conditions and the construction of related shape functions in the boundary type methods, but are only for evaluation of the domain’s influences on the boundary unknowns. Techniques of using Cartesian grids are developed and combined with the newly developed boundarytype numerical method, the boundary point method, to solve the Poisson equations. Several numerical examples are presented to show feasibility and accuracy of the proposed algorithm. The effects of the relation between spacing of Cartesian grids and the support of the boundary points on accuracy are investigated in the computations.

Key words: boundary integral equation; domain integral; Cartesian grids; boundary point method; Poisson equation