Combined Optimized Domain Decomposition Method and a Modified Fixed Point Method for Non Linear Diffusion Equation

Authors

M. R. Amattouch, Department of mathematics, Faculty of sciences and techniques, University of Abdelmalek Essaadi, BP.416, Tangier, MoroccoFollow
H. Belhadj, Department of mathematics, Faculty of sciences and techniques, University of Abdelmalek Essaadi, BP.416, Tangier, MoroccoFollow

Author Country (or Countries)

Morocco

Abstract

This work is devoted to an optimized domain decomposition method applied to a non linear anisotropic reaction equation. The proposed method is based on the idea of the optimized of two order (OO2) method developed this last two decades. We first use a modified fixed point technique to linearize the problem in a way to converge fately, then we generalize the OO2 method and modify it to obtain a new more optimized rate of convergence of the Schwarz algorithm. To compute the new rate of convergence we have used Fourier analysis. For the numerical computation we minimize this rate of convergence using a global optimization algorithm. Several test-cases of analytical problems illustrate this approach and show the efficiency of the proposed new method.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/110125

Recommended Citation

R. Amattouch, M. and Belhadj, H. (2017) "Combined Optimized Domain Decomposition Method and a Modified Fixed Point Method for Non Linear Diffusion Equation," Applied Mathematics & Information Sciences: Vol. 11: Iss. 1, Article 25.
DOI: http://dx.doi.org/10.18576/amis/110125
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss1/25