Journal ArticleDOI
Matrix decomposition RBF algorithm for solving 3D elliptic problems
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TLDR
The collocation points are placed on concentric spheres and thus the resulting global matrix possesses a block circulant structure, which is exploited to develop an efficient matrix decomposition algorithm for the solution of the resulting system.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.read more
Citations
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Journal ArticleDOI
A localized approach for the method of approximate particular solutions
TL;DR: A localized scheme for the method of approximate particular solutions (LMAPS) is developed that allows the use of a small neighborhood of points to find the approximate solution of the given partial differential equation.
Journal ArticleDOI
A comparison of three explicit local meshless methods using radial basis functions
TL;DR: In this article, three kinds of explicit local meshless methods are compared: the local method of approximate particular solutions (LMAPS), the local direct radial basis function collocation method (LDRBFCM), and the local indirect radial basis functions collocation (LIRBFCMs) and the five-noded sub-domains are used in localization.
Journal ArticleDOI
Matrix decomposition algorithms for elliptic boundary value problems: a survey
TL;DR: An overview of matrix decomposition algorithms (MDAs) for the solution of systems of linear equations arising when various discretization techniques are applied in the numerical solution of certain separable elliptic boundary value problems in the unit square is provided.
Journal ArticleDOI
Regularized meshless method for nonhomogeneous problems
Wen Chen,Ji Lin,Fuzhang Wang +2 more
TL;DR: In this paper, the authors apply the regularized meshless method to the nonhomogeneous problems in conjunction with the dual reciprocity technique in the evaluation of the particular solution and demonstrate the accuracy and efficiency of the present strategy.
Journal ArticleDOI
Kansa-RBF Algorithms for Elliptic Problems in Axisymmetric Domains
TL;DR: A Kansa-radial basis function method is employed for the numerical solution of elliptic boundary value problems in three-dimensional axisymmetric domains and considers problems governed by the Poisson inequality.
References
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Journal ArticleDOI
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
Youcef Saad,Martin H. Schultz +1 more
TL;DR: An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace.
Book
Matrix Analysis and Applied Linear Algebra
TL;DR: The author presents Perron-Frobenius theory of nonnegative matrices Index, a theory of matrices that combines linear equations, vector spaces, and matrix algebra with insights into eigenvalues and Eigenvectors.
Journal ArticleDOI
BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems
TL;DR: Numerical experiments indicate that the new variant of Bi-CG, named Bi- CGSTAB, is often much more efficient than CG-S, so that in some cases rounding errors can even result in severe cancellation effects in the solution.
Journal ArticleDOI
Scattered data interpolation: tests of some methods
TL;DR: In this paper, the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods are presented. But the evaluation process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation.