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 masking procedure. In addition level dependent thresholding were introduced to improve the efficiency and convergence rate of the solution. We will show how the generalized wavelet based adaptive method can be applied for detecting nearly singularities in Poisson type PDEs over irregular domains. The numerical examples have illustrated that the proposed method is powerful to analyze the Poisson type PDEs with rapid changes in gradients and nearly singularities.


Civil, Architectural and Environmental Engineering

Keywords and Phrases

Adaptive node refinement; Irregular domain; Meshless; Multiquadrics; Nearly singular PDEs; Poisson-type equation; RBF collocation; Wavelet decomposition

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2009 Tech Science Press, All rights reserved.

Publication Date

01 Feb 2009