A meshless polyharmonic-type boundary interpolation method for solving boundary integral equations

被引:11
作者
Gáspár, C [1 ]
机构
[1] Szechenyi Istvan Univ, Dept Math, H-9007 Gyor, Hungary
基金
匈牙利科学研究基金会;
关键词
meshless methods; scattered data interpolation; biharmonic interpolation; polyharmonic interpolation; quadtree;
D O I
10.1016/j.enganabound.2003.04.001
中图分类号
T [工业技术];
学科分类号
08 [工学];
摘要
A boundary interpolation technique is introduced based on multi-elliptic partial differential equations. The interpolation problem is converted to a special higher order partial differential equation which is completely independent of the geometry of the original problem. Based on this interpolation method, meshless methods are constructed for the 2D Laplace-Poisson equation. The presented approach makes it possible to avoid solving large and dense interpolation equations. The auxiliary higher order partial differential equation is solved by robust, quadtree-based multi-level methods. The results can be easily generalized to 3D problems as well. (C) 2004 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1207 / 1216
页数:10
相关论文
共 28 条
[1]
Alves CJS, 2002, ADV BOUND ELEM, V13, P67
[2]
Fast evaluation of radial basis functions: Methods for two-dimensional polyharmonic splines [J].
Beatson, RK ;
Light, WA .
IMA JOURNAL OF NUMERICAL ANALYSIS, 1997, 17 (03) :343-372
[3]
FAM GSA, 2002, INT SERIES ADV BOUND, P297
[4]
Solving differential equations with radial basis functions: multilevel methods and smoothing [J].
Fasshauer, GE .
ADVANCES IN COMPUTATIONAL MATHEMATICS, 1999, 11 (2-3) :139-159
[5]
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
[6]
Solving partial differential equations by collocation using radial basis functions [J].
Franke, C ;
Schaback, R .
APPLIED MATHEMATICS AND COMPUTATION, 1998, 93 (01) :73-82
[7]
SCATTERED DATA INTERPOLATION - TESTS OF SOME METHODS [J].
FRANKE, R .
MATHEMATICS OF COMPUTATION, 1982, 38 (157) :181-200
[8]
A multipole expansion technique in solving boundary integral equations [J].
Gaspar, C .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1998, 157 (3-4) :289-297
[9]
Multi-level biharmonic and bi-Helmholtz interpolation with application to the boundary element method [J].
Gáspár, C .
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2000, 24 (7-8) :559-573
[10]
Gáspár C, 2003, LECT NOTES COMP SCI, V26, P143