Matrix Decomposition RBF Algorithm for Solving 3D Elliptic Problems
Document Type
Article
Publication Date
12-1-2009
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
In this study, we propose an efficient algorithm for the evaluation of the particular solutions of three-dimensional inhomogeneous elliptic partial differential equations using radial basis functions. The collocation points are placed on concentric spheres and thus the resulting global matrix possesses a block circulant structure. This structure is exploited to develop an efficient matrix decomposition algorithm for the solution of the resulting system. Further savings in the matrix decomposition algorithm are obtained by the use of fast Fourier transforms. The proposed algorithm is used, in conjunction with the method of fundamental solutions for the solution of three-dimensional inhomogeneous elliptic boundary value problems. (C) 2009 Elsevier Ltd. All rights reserved.
Publication Title
Engineering Analysis With Boundary Elements
Volume
33
Issue
12
First Page
1368
Last Page
1373
Recommended Citation
Karageorghis, A.,
Chen, C.,
Smyrlis, Y.
(2009). Matrix Decomposition RBF Algorithm for Solving 3D Elliptic Problems. Engineering Analysis With Boundary Elements, 33(12), 1368-1373.
Available at: https://aquila.usm.edu/fac_pubs/1139