On Convergence of a Least-Squares Kansa's Method for the Modified Helmholtz Equations

被引：0

作者：

Kwok, Ting-On ^{[1
]}

Ling, Leevan ^{[1
]}

机构：

[1] Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China

来源：

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2009年 / 1卷 / 03期

关键词：

Radial basis function; adaptive greedy algorithm; asymmetric collocation; Kansa's method; convergence analysis; RADIAL BASIS FUNCTIONS; PARTIAL-DIFFERENTIAL-EQUATIONS; COMPUTATIONAL FLUID-DYNAMICS; MESHLESS COLLOCATION METHODS; DATA APPROXIMATION SCHEME; DECOMPOSITION; MULTIQUADRICS; BOUNDS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze a least-squares asymmetric radial basis function collocation method for solving the modified Helmholtz equations. In the theoretical part, we proved the convergence of the proposed method providing that the collocation points are sufficiently dense. For numerical verification, direct solver and a sub-space selection process for the trial space (the so-called adaptive greedy algorithm) is employed, respectively, for small and large scale problems.

引用

页码：367 / 382

页数：16

共 24 条

[1]

[Anonymous], 2007, MESHFREE APPROXIMATI

[2]

[Anonymous], 1988, Approx. Theory Appl

[3]

[Anonymous], 2003, RADIAL BASIS FUNCTIO

[4]

[Anonymous], 2005, Cambridge Monograph, Applied Comput. Math.

[5] On approximate cardinal preconditioning methods for solving PDEs with radial basis functions [J].

Brown, D ;

Ling, L ;

Kansa, E ;

Levesley, J .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2005, 29 (04) :343-353

[6] Error estimates of local multiquadric-based differential quadrature (LMQDQ) method through numerical experiments [J].

Ding, H ;

Shu, C ;

Tang, DB .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2005, 63 (11) :1513-1529

[7] On unsymmetric collocation by radial basis functions [J].

Hon, YC ;

Schaback, R .

APPLIED MATHEMATICS AND COMPUTATION, 2001, 119 (2-3) :177-186

[8] MULTIQUADRICS - A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS .1. [J].

KANSA, EJ .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1990, 19 (8-9) :127-145

[9] MULTIQUADRICS - A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS .2. SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL-DIFFERENTIAL EQUATIONS [J].

KANSA, EJ .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1990, 19 (8-9) :147-161

[10]

LEE CF, 2007, ADV COMPUT IN PRESS

← 1 2 3 →