A Survey of Boundary Integral Equation Methods for the Numerical Solution of Laplace’s Equation in Three Dimensions
A Survey of Boundary Integral Equation Methods for the Numerical Solution of Laplace’s Equation in Three Dimensions
复制标题
三维拉普拉斯方程数值解的边界积分方程方法综述
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
K. Atkinson
中科院分区：
文献类型：
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作者：
K. Atkinson
介绍了将拉普拉斯方程转化为边界积分方程的主要方法，并讨论了它们的可解性和解的正则性。边界积分方程的数值求解方法根据其使用的是局部逼近函数还是全局逼近函数、是配点法还是Galerkin法以及求解的方程是定义在边界光滑的区域上还是仅定义在边界分段光滑的区域上进行了分类。这些数值方法的数学分析中的一些主要思想进行了概述。某些问题与边界积分方程的所有数值方法有关。其中主要是数值积分和线性方程组的迭代解。这些主题的研究文献，因为它们出现在解决BIE的审查，并讨论了一些主要的想法。
The principal reformulations of Laplace’s equation as boundary integral equations (BIEs) are described, together with results on their solvability and the regularity of their solutions. The numerical methods for solving BIEs are categorized, based on whether the method uses local or global approximating functions, whether the method is of collocation or Galerkin type, and whether the equation being solved is defined on a region whose boundary is smooth or only piecewise smooth. Some of the major ideas in the mathematical analysis of these numerical methods are outlined. Certain problems are associated with all numerical methods for boundary integral equations. Principal among these are numerical integration and the iterative solution of linear systems of equations. The research literature for these topics as they arise in solving BIEs is reviewed, and some of the major ideas are discussed.