Domain Decomposition Method for a Class of Non-Linear Elliptic Equation with Arbitrary Growth Nonlinearity and Data Measure

2004 ◽  
pp. 79-88
Author(s):  
Nour Eddine Alaa ◽  
Jean Rodolphe Roche
Keyword(s):  
Elliptic Equation ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Linear Elliptic Equation ◽  
Non Linear

scholarly journals Optimized Domain Decomposition Method for Non Linear Reaction Advection Diffusion Equation

2016 ◽  
Vol 12 (27) ◽  
pp. 63 ◽  
Author(s):  
M.R. Amattouch ◽  
N. Nagid ◽  
H. Belhadj
Keyword(s):  
Diffusion Equation ◽  
Domain Decomposition ◽  
Rate Of Convergence ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Linear Reaction ◽  
Non Linear ◽  
Schwarz Algorithm

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.

scholarly journals A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics

2020 ◽  
Vol 369 ◽  
pp. 113223
Author(s):  
Alice Lieu ◽  
Philippe Marchner ◽  
Gwénaël Gabard ◽  
Hadrien Bériot ◽  
Xavier Antoine ◽  
...  
Keyword(s):  
Finite Elements ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
High Order ◽  
Overlapping Schwarz
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