Article
Stable PDE Solution Methods for Large Multiquadric Shape Parameters
CMES - Computer Modeling in Engineering and Sciences
Abstract
We present a new method based upon the paper of Volokh and Vilney (2000) that produces highly accurate and stable solutions to very ill-conditioned multiquadric (MQ) radial basis function (RBF) asymmetric collocation methods for partial differential equations (PDEs). We demonstrate that the modified Volokh-Vilney algorithm that we name the improved truncated singular value decomposition (IT-SVD) produces highly accurate and stable numerical solutions for large values of a constant MQ shape parameter, c, that exceeds the critical value of c based upon Gaussian elimination.
Department(s)
Civil, Architectural and Environmental Engineering
Keywords and Phrases
- Asymmetric collocation,
- Improved truncated singular value decomposition,
- Meshless radial basis functions,
- Multiquadric,
- Partial differential equations
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2008 Tech Science Press, All rights reserved.
Publication Date
1-1-2008
Publication Date
01 Jan 2008
Disciplines
Citation Information
Nicolas Ali Libre, Arezoo Emdadi, Edward J. Kansa, Mohammad Rahimian, et al.. "Stable PDE Solution Methods for Large Multiquadric Shape Parameters" CMES - Computer Modeling in Engineering and Sciences Vol. 25 Iss. 1 (2008) p. 23 - 41 ISSN: 1526-1492 Available at: http://works.bepress.com/arezoo-emdadi/9/