Comparison Of Two Solvers For The Extended
Method Of Fundamental Solutions
Author(s)
R. Gospavic, N. Haque, V. Popov & C. S. Chen
Abstract
In this work two solvers are compared for solution of the system of equations
arising from the extended method of fundamental solutions. This method is a
combination of the method of fundamental solutions (MFS) and the dual
reciprocity method (DRM). The stationary and non-stationary elliptic partial
differential equations with variable coefficients are considered. For the nonstationary
case a finite difference time discretisation is used. Two sets of basis
functions are used, a fundamental solution for the considered operator and a
radial basis function (RBF) approximation for the particular solution, in
particular the multiquadric (MQ) functions. A direct solver using a high number
of digits and an indirect solver based on truncated singular value decomposition
(TSVD) were used and compared. The method is tested for different values of
the shape parameter in the MQ basis functions.
Keywords: meshless, method of fundamental solutions, elliptic partial
differential equations, non-stationary problems.
1 Introduction
In recent times there has been growing interest in developing various
meshless methods for the numerical solution of partial differential equations
(PDEs) [1–3]. The major advantage of the meshless methods compared to the
traditional numerical methods for solving PDEs is that they avoid the
difficulties of meshing the domain and boundary, which is especially
beneficial for 3D problems [2]. The use of meshless methods simplifies the
geometrical representation of the problem domain and eliminates the need
Keywords
meshless, method of fundamental solutions, elliptic partial
differential equations, non-stationary problems.
Related Book
Other papers in this volume
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