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Stable PDE Solution Methods for Large Multiquadric Shape Parameters

Arezoo Emdadi1, Edward J. Kansa2, Nicolas Ali Libre1,3, Mohammad Rahimian1, Mohammad Shekarchi1
Department of Civil Engineering, University of Tehran, Tehran, Iran
E.J. Kansa*, Department of Mechanical and Aeronautical Engineering, University of California, Davis, Davis, CA95616-5294 USA. email: ejkansa@ucdavis.edu
Corresponding author, Nicolas Ali Libre, email : nalibre@ut.ac.ir

Computer Modeling in Engineering & Sciences 2008, 25(1), 23-42. https://doi.org/10.3970/cmes.2008.025.023

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.

Keywords

meshless radial basis functions, multiquadric, asymmetric collocation, partial differential equations, improved truncated singular value decomposition

Cite This Article

Emdadi, A., Kansa, E. J., Libre, N. A., Rahimian, M., Shekarchi, M. (2008). Stable PDE Solution Methods for Large Multiquadric Shape Parameters. CMES-Computer Modeling in Engineering & Sciences, 25(1), 23–42.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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