Schwarz waveform relaxation algorithms for some semilinear reaction-advection-diffusion type equations
 
 
Description:  We are interested in domain decomposition algorithms of Schwarz waveform relaxation type to compute approximate solutions of some nonlinear evolution equations. Schwarz waveform relaxation algorithms are based on a decomposition of the problem in space, like classical Schwarz methods, but they solve subdomain problems in both space and time. This approach is suitable for parallelization and allows us to use different time and space grids in each subdomains. For the model problem of a semilinear reaction-diffusion equation, we define linear and nonlinear Robin and Ventcel transmission conditions between the subdomains, which lead to a well defined algorithm. The nonlinear conditions are based on best approximation problems for the linear equation and provide an efficient algorithm, as we can see by the numerical results that we present. We show the well-posedness and the convergence of the algorithms. We present at the end an extension to the reactive transport system, which is a model problem encountered in geological CO_2 storage modeling.
Date:  2010-10-27
Start Time:   14:00
Speaker:  Filipa Caetano (Univ. Paris-Sud 11, France)
Institution:  Université Paris-Sud 11
Place:  Room 5.5
Research Groups: -Numerical Analysis and Optimization
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