scholarly journals An iteration-by-subdomain overlapping Dirichlet/Robin domain decomposition method for advection–diffusion problems

2003 ◽  
Vol 158 (2) ◽  
pp. 243-276 ◽  
Author(s):  
Guillaume Houzeaux ◽  
Ramon Codina
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Advection Diffusion ◽  
Diffusion Problems

ON THE ELLIPTIC-HYPERBOLIC COUPLING I: THE ADVECTION-DIFFUSION EQUATION VIA THE χ-FORMULATION

1993 ◽  
Vol 03 (02) ◽  
pp. 145-170 ◽  
Author(s):  
C. CANUTO ◽  
A. RUSSO
Keyword(s):  
Diffusion Equation ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Advection Equation ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Subdomain Method ◽  
Self Adaptive

An advection-diffusion equation is considered, for which the solution is advection-dominated in most of the domain. A domain decomposition method based on a self-adaptive, smooth coupling of the reduced advection equation and the full advection-diffusion equation is proposed. The convergence of an iteration-by-subdomain method is investigated.

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.

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