Solution to the Dirichlet Problem on Irregular Domains Using Wavelet-Based Approach
Francis Ohene Boateng *
Department of Mathematics Education, University of Education, Winneba, Kumasi, Ghana.
Joseph Ackora-Prah
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
Anthony Y. Aidoo
Department of Mathematics and Computer Science, Eastern Connecticut State University, Willimantic, USA.
*Author to whom correspondence should be addressed.
Abstract
We present a Finite Difference Fictitious Domain Wavelet Method (FDFDWM) with penalty for solving two dimensional (2D) Dirichlet problem for linear elliptic PDE on irregular geometric domains. In this method, the 2-D Dirichlet problem is discretized along one of the spatial variables, reducing it to a 1-D problem. The problem and the boundaries of the irregular domain are approximated using compactly supported wavelets. Results from the numerical analysis indicate that, our method performs better in terms of accuracy and convergence of the approximate solution compared with finite element method.
Keywords: Dirichlet problem, penalty, fictitious domain, PDEs, Daubechies wavelet function, irregular domain, finite difference