Chebyshev tau matrix method for Poisson-type equations in irregular domain

被引：21

作者：

Kong, Weibin ^{[1
]}

Wu, Xionghua ^{[1
]}

机构：

[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2009年 / 228卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Chebyshev tau matrix method; Poisson-type equation; Irregular domain; Meshless;

D O I：

10.1016/j.cam.2008.09.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a new meshless method, Chebyshev tau matrix method (CTMM) is researched. The matrix representations for the differentiation and multiplication of Chebyshev expansions make CTMM easy to implement. Problems with curve boundary can be efficiently treated by CTMM. Poisson-type problems, including standard Poisson problems, Helmholtz problems, problems with variable coefficients and nonlinear problems are computed. Some numerical experiments are implemented to verify the efficiency of CTMM, and numerical results are in good agreement with the analytical one. It appears that CTMM is very effective for Poisson-type problems in irregular domains. (c) 2008 Elsevier B.V. All rights reserved.

引用

页码：158 / 167

页数：10

共 11 条

[1]

[Anonymous], 1994, NUMER METHOD PARTIAL, DOI DOI 10.1002/NUM.1690100503

[2] DOMAIN IMBEDDING METHODS FOR THE STOKES EQUATIONS [J].

BORGERS, C .

NUMERISCHE MATHEMATIK, 1990, 57 (05) :435-451

[3] Spectral smoothed boundary methods:: The role of external boundary conditions [J].

Bueno-Orovio, A ;

Pérez-García, VM .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2006, 22 (02) :435-448

[4]

CANUTO C, 2006, SCIENTIF COMPUT, P3, DOI 10.1007/978-3-540-30726-6

[5] A spectral embedding method applied to the advection-diffusion equation [J].

Elghaoui, M ;

Pasquetti, R .

JOURNAL OF COMPUTATIONAL PHYSICS, 1996, 125 (02) :464-476

[6] SPECTRAL INTEGRATION AND 2-POINT BOUNDARY-VALUE-PROBLEMS [J].

GREENGARD, L .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1991, 28 (04) :1071-1080

[7]

Lanczos C, 1938, J Math Phys, V17, P123, DOI [DOI 10.1002/SAPM1938171123, 10.1002/sapm1938171123]

[8]

Mason J.C., 2003, Chebyshev polynomials, DOI 10.1201/9781420036114

[9] A meshless method for generalized linear or nonlinear Poisson-type problems [J].

Wang, Hui ;

Qin, Qing-Hua .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2006, 30 (06) :515-521

[10] Differential quadrature domain decomposition method for problems on a triangular domain [J].

Wu, XH ;

Liu, S .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2005, 21 (03) :574-585

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