Neumann problems of 2D Laplace's equation by method of fundamental solutions
Neumann problems of 2D Laplace's equation by method of fundamental solutions
复制标题
DOI：
10.1016/j.apnum.2017.04.004
复制
发表时间：
2017-09
影响因子：
2.8
通讯作者：
Zi-Cai Li;Ming-Gong Lee;Hung‐Tsai Huang;J. Chiang
中科院分区：
文献类型：
--
作者：
Zi-Cai Li;Ming-Gong Lee;Hung‐Tsai Huang;J. Chiang
The method of fundamental solutions (MFS) was first used by Kupradze in 1963 [21]. Since then, there have appeared numerous reports of the MFS. Most of the existing analysis for the MFS are confined to Dirichlet problems on disk domains. It seems to exist no analysis for Neumann problems. This paper is devoted to Neumann problems in non-disk domains, and the new stability analysis and the error analysis are made. The bounds for both condition numbers and errors are derived in detail. The optimal convergence rates in L 2 and H 1 norms in S are achieved, and the condition number grows exponentially as the number of fundamental functions increases. To reduce the huge condition numbers, the truncated singular value decomposition (TSVD) may be solicited. Numerical experiments are provided to support the analysis made. The analysis for Neumann problems in this paper is intriguing due to its distinct features.
