Optimized Domain Decomposition Method for Non Linear Reaction Advection Diffusion Equation

  • M.R. Amattouch University of Abdelmalek Essaadi, Faculty Of Sciences And Techniques, Department Of Mathematics, Tangier, Morocco
  • N. Nagid University of Abdelmalek Essaadi, Faculty Of Sciences And Techniques, Department Of Mathematics, Tangier, Morocco
  • H. Belhadj University of Abdelmalek Essaadi, Faculty Of Sciences And Techniques, Department Of Mathematics, Tangier, Morocco

Abstract

This work is devoted to an optimized domain decomposition method applied to a non linear reaction advection diffusion equation. The proposed method is based on the idea of the optimized of two order (OO2) method developed this last two decades. We first treat a modified fixed point technique to linearize the problem and 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.

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Published
2016-09-30
How to Cite
Amattouch, M., Nagid, N., & Belhadj, H. (2016). Optimized Domain Decomposition Method for Non Linear Reaction Advection Diffusion Equation. European Scientific Journal, ESJ, 12(27), 63. https://doi.org/10.19044/esj.2016.v12n27p63