T. Tsangaris¹, Y.–S. Smyrlis^{1, 2}, A. Karageorghis^{1, 2}

CMC-Computers, Materials & Continua, Vol.1, No.3, pp. 245-258, 2004, DOI:10.3970/cmc.2004.001.245

Abstract The Method of Fundamental Solutions (MFS) is a boundary-type method for the solution of certain elliptic boundary value problems. In this work, we develop an efficient matrix decomposition MFS algorithm for the solution of biharmonic problems in annular domains. The circulant structure of the matrices involved in the MFS discretization is exploited by using Fast Fourier Transforms. The algorithm is tested numerically on several examples. More >

Yiorgos-Sokratis Smyrlis¹, Andreas Karageorghis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 535-550, 2003, DOI:10.3970/cmes.2003.004.535

Abstract In this study, we investigate the application of the Method of Fundamental Solutions for the solution of biharmonic Dirichlet problems on a disk. Modifications of the method for overcoming sources of inaccuracy are suggested. We also propose an efficient algorithm for the solution of the resulting systems which exploits the symmetries of the matrices involved. The techniques described in the paper are applied to standard test problems. More >

M.A. Golberg¹, C.S. Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.1, pp. 87-96, 2001, DOI:10.3970/cmes.2001.002.087

Abstract The purpose of this paper is to develop a highly efficient mesh-free method for solving nonlinear diffusion-reaction equations in R^d, d=2, 3. Using various time difference schemes, a given time-dependent problem can be reduced to solving a series of inhomogeneous Helmholtz-type equations. The solution of these problems can then be further reduced to evaluating particular solutions and the solution of related homogeneous equations. Recently, radial basis functions have been successfully implemented to evaluate particular solutions for Possion-type equations. A more general approach has been developed in extending this capability to obtain particular solutions for Helmholtz-type equations More >