1. Matrix decomposition RBF algorithm for solving 3D elliptic problems
- Author
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Karageorghis, Andreas, Chen, C. S., Smyrlis, Yiorgos-Sokratis, Karageorghis, Andreas [0000-0002-8399-6880], and Smyrlis, Yiorgos-Sokratis [0000-0001-9126-2441]
- Subjects
Elliptic problem ,Eight-point algorithm ,MathematicsofComputing_NUMERICALANALYSIS ,Geometry ,Particular solution ,Matrix decomposition ,law.invention ,Radial basis functions ,law ,Singular value decomposition ,Method of fundamental solutions ,Global matrix ,Block circulant ,Concentric spheres ,Fast Fourier transforms ,Mathematics ,Efficient algorithm ,Image segmentation ,Applied Mathematics ,Three dimensional ,Collocation points ,General Engineering ,Block matrix ,Elliptic boundary value problem ,Radial basis function networks ,Partial differential equations ,LU decomposition ,QR decomposition ,Computational Mathematics ,Elliptic partial differential equation ,Algorithm ,Algorithms ,Analysis - 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. © 2009 Elsevier Ltd. All rights reserved. 33 12 1368 1373 Cited By :17
- Published
- 2009