Title: Radial function collocation solution of partial differential equations in irregular domains

Authors: V. Pereyra, G. Scherer, P. Gonzalez Casanova

Addresses: Weidlinger Associates Inc., 399 W., El Camino Real #200, Mountain View, CA, USA. ' Department of Mathematics, University of Reading, UK. ' UNAM, Mexico DF.

Abstract: We consider a collocation method using radial functions for the solution of partial differential equations in irregular domains. We use a regularised least squares approach to solve the potentially ill-conditioned problems that may arise. This meshless method is easy to implement and eliminates most of the problems that mesh oriented methods have with irregular boundaries and complicated domains. When solving, also, for the position and shape parameters of the radial functions we obtain an adaptive, albeit non-linear, method. In this case, the resulting problem is a separable non-linear least squares one that can be efficiently solved by the Variable Projection method.

Keywords: elliptic problems; collocation; meshless methods; TSVD; variable projections; radial functions; partial differential equations; irregular domains; regularised least squares; nonlinear least squares.

DOI: 10.1504/IJCSM.2007.013762

International Journal of Computing Science and Mathematics, 2007 Vol.1 No.1, pp.28 - 41

Published online: 25 May 2007 *

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