Nicolas Ali Libre1,2, Arezoo Emdadi2, Edward J. Kansa3,4, Mohammad Shekarchi2, Mohammad Rahimian2
CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 263-284, 2008, DOI: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… More >
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