Domain decomposition by radial basis functions for time dependent partial differential equations

Authors:
José Antonio Muñoz-Gómez;Pedro González-Casanova;Gustavo Rodríguez-Gómez
Affiliations:
Ciencias Computacionales, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Puebla, Tonantzintla, México;UICA-DGSCA, Universidad Nacional Autónoma de México, D.F., México;Ciencias Computacionales, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Puebla, Tonantzintla, México
Venue:
ACST'06 Proceedings of the 2nd IASTED international conference on Advances in computer science and technology
Year:
2006

Citing 3
Cited 3

Domain decomposition: parallel multilevel methods for elliptic partial differential equations

Domain decomposition: parallel multilevel methods for elliptic partial differential equations
A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs

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Overlapping domain decomposition method by radial basis functions

Applied Numerical Mathematics

Radial function collocation solution of partial differential equations in irregular domains

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The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems

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An adaptive domain decomposition method for the Hamilton---Jacobi---Bellman equation

Journal of Global Optimization

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Abstract

In the last years, there has been an increased investigation of efficient algorithms to solve problems of great scale. The main restriction of the traditional methods, like finite difference methods and finite element methods, is the mesh generation. In this work, we investigate the overlapping domain decomposition method applied to time dependent partial differential equations with unsymmetric radial basis function collocation method. Numerical experiments performed with thin-plate splines as kernel function, for an evolutionary problem in two dimensions, show a drastic time reduction as we increase the number of subdomains, high numerical accuracy and lower numerical diffusion. The numerical results suggest that the scheme proposed can be useful to tackle large scale time dependent problems.