Open AccessOptimized Domain Decomposition Method for Non Linear Reaction Advection Diffusion Equation
Author(s) -
Mohamed Ridouan Amattouch,
Nabila Nagid,
Hassan Belhadj
Publication year - 2016
Publication title -
european scientific journal
Language(s) - English
Resource type - Journals
eISSN - 1857-7881
pISSN - 1857-7431
DOI - 10.19044/esj.2016.v12n27p63
Subject(s) - rate of convergence , convergence (economics) , domain decomposition methods , computation , advection , mathematics , domain (mathematical analysis) , algorithm , mathematical optimization , diffusion , computer science , mathematical analysis , key (lock) , finite element method , physics , computer security , economics , thermodynamics , economic growth
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.