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    Wavelet Based Adaptive RBF Method for Nearly Singular Poisson-Type Problems on Irregular Domains

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

    CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 161-190, 2009, DOI:10.3970/cmes.2009.050.161

    Abstract We present a wavelet based adaptive scheme and investigate the efficiency of this scheme for solving nearly singular potential PDEs over irregularly shaped domains. For a problem defined over Ω∈ℜd, the boundary of an irregularly shaped domain, Γ, is defined as a boundary curve that is a product of a Heaviside function along the normal direction and a piecewise continuous tangential curve. The link between the original wavelet based adaptive method presented in Libre, Emdadi, Kansa, Shekarchi, and Rahimian (2008, 2009) or LEKSR method and the generalized one is given through the use of simple Heaviside More >

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