Table of Content

Open Access iconOpen Access

ARTICLE

A Fast Adaptive Wavelet scheme in RBF Collocation for nearly singular potential PDEs

Nicolas Ali Libre1,2, Arezoo Emdadi2, Edward J. Kansa3,4, Mohammad Shekarchi2, Mohammad Rahimian2

Corresponding author. Tel: +9821-88973631, Fax: +9821-88959740, Email: nalibre@ut.ac.ir, URL: www.libre.ir/en
School of Civil Engineering, University of Tehran, Tehran, Iran
Department of Mechanical and Aeronautical Engineering, University of California-Davis, Davis, CA 95616 USA
Corresponding author. Email: ejkansa@ucdavis.edu

Computer Modeling in Engineering & Sciences 2008, 38(3), 263-284. https://doi.org/10.3970/cmes.2008.038.263

Abstract

We present a wavelet based adaptive scheme and investigate the efficiency of this scheme for solving nearly singular potential PDEs. Multiresolution wavelet analysis (MRWA) provides a firm mathematical foundation by projecting the solution of PDE onto a nested sequence of approximation spaces. The wavelet coefficients then were used as an estimation of the sensible regions for node adaptation. The proposed adaptation scheme requires negligible calculation time due to the existence of the fast Discrete Wavelet Transform (DWT). Certain aspects of the proposed adaptive scheme are discussed through numerical examples. It has been shown that the proposed adaptive scheme can detect the singularities both in the domain and near the boundaries. Moreover, the proposed adaptive scheme can be utilized for capturing the regions with high gradient both in the solution and its spatial derivatives. Due to the simplicity of the proposed method, it can be efficiently applied to large scale nearly singular engineering problems.

Keywords


Cite This Article

APA Style
Libre, N.A., Emdadi, A., Kansa, E.J., Shekarchi, M., Rahimian, M. (2008). A fast adaptive wavelet scheme in RBF collocation for nearly singular potential pdes. Computer Modeling in Engineering & Sciences, 38(3), 263-284. https://doi.org/10.3970/cmes.2008.038.263
Vancouver Style
Libre NA, Emdadi A, Kansa EJ, Shekarchi M, Rahimian M. A fast adaptive wavelet scheme in RBF collocation for nearly singular potential pdes. Comput Model Eng Sci. 2008;38(3):263-284 https://doi.org/10.3970/cmes.2008.038.263
IEEE Style
N.A. Libre, A. Emdadi, E.J. Kansa, M. Shekarchi, and M. Rahimian "A Fast Adaptive Wavelet scheme in RBF Collocation for nearly singular potential PDEs," Comput. Model. Eng. Sci., vol. 38, no. 3, pp. 263-284. 2008. https://doi.org/10.3970/cmes.2008.038.263



cc 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.
  • 1296

    View

  • 1011

    Download

  • 0

    Like

Share Link