Solution to the Dirichlet Problem on Irregular Domains Using Wavelet-Based Approach
Francis Ohene Boateng, Joseph Ackora-Prah, Anthony Y. Aidoo
Journal of Advances in Mathematics and Computer Science · pp. 1–14 · Published 31 Dec 2018
10.9734/JAMCS/2019/45965Abstract
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.
Cited by 1
Vida Afosaa, Anthony Y. Aidoo, Nicholas Kwasi-Do Ohene Opoku · Journal of Applied Mathematics · 2025
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