Radial basis functions for solving near singular Poisson problems

被引：20

作者：

Chen, CS ^{[1
]}

Kuhn, G

Li, J

Mishuris, G

机构：

[1] Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA

[2] Univ Erlangen Nurnberg, Inst Appl Mech, Nurnberg, Germany

[3] Rzeszow Univ Technol, Dept Math, PL-35959 Rzeszow, Poland

来源：

COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING | 2003年 / 19卷 / 05期

关键词：

radial basis functions; near singular problems; dual reciprocity method; method of fundamental solutions; compactly supported radial basis functions; particular solution;

D O I：

10.1002/cnm.593

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we investigate the use of radial basis functions for solving Poisson problems with a near-singular inhomogeneous source term. The solution of the Poisson problem is first split into two parts: near-singular solution and smooth solution. A method for evaluating the near-singular particular solution is examined. The smooth solution is further split into a particular solution and a homogeneous solution. The MPS-DRM approach is adopted to evaluate the smooth solution. Copyright (C) 2003 John Wiley Sons, Ltd.

引用

页码：333 / 347

页数：15

共 30 条

[1]

Amini S., 1989, J INTEGRAL EQU APPL, P1

[2]

[Anonymous], 1992, J NUM METHOD PART DI

[3]

[Anonymous], 1992, DUAL RECIPROCITY BOU

[4]

ATKINSON KE, 1990, NUMERICAL SOLUTION I, pCH1

[5]

Chen CS, 1999, COMMUN NUMER METH EN, V15, P137, DOI 10.1002/(SICI)1099-0887(199902)15:2<137::AID-CNM233>3.0.CO

[6]

2-9

[7] The method of fundamental solutions for elliptic boundary value problems [J].

Fairweather, G ;

Karageorghis, A .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 1998, 9 (1-2) :69-95

[8]

FAIRWEATHER G, 1987, J COMPUT PHYS, V69, P435

[9] Solving differential equations with radial basis functions: multilevel methods and smoothing [J].

Fasshauer, GE .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 1999, 11 (2-3) :139-159

[10] Multistep scattered data interpolation using compactly supported radial basis functions [J].

Floater, MS ;

Iske, A .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1996, 73 (1-2) :65-78

← 1 2 3 →