Geodesic
Toward an optimized global-in-time Schwarz algorithm for diffusion equations with discontinuous and spatially variable coefficients. II: The variable coefficients case
Electronic transactions on numerical analysis, Tome 40 (2013), pp. 170-186.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This paper is the second part of a study dealing with the application of a global-in-time Schwarz method to a one-dimensional diffusion problem defined on two non-overlapping subdomains. In the first part, we considered the case that the diffusion coefficients were constant and possibly discontinuous. In the present study, we address the problem for spatially variable coefficients with a discontinuity at the interface between subdomains. For this particular case, we derive a new approach to analytically determine the convergence factor of the associated algorithm. The theoretical results are illustrated by numerical experiments with $Dirichlet-Neumann$ and $Robin-Robin$ interface conditions. In the $Robin-Robin$ case, thanks to the convergence factor found at the analytical level, we can optimize the convergence speed of the Schwarz algorithm.
Classification : 65M55, 65F10, 65N22, 35K15, 76F40
Keywords: optimized Schwarz methods, waveform relaxation, alternating and parallel Schwarz methods 
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     author = {Lemari\'e, Florian and Debreu, Laurent and Blayo, Eric},
     title = {Toward an optimized global-in-time {Schwarz} algorithm for diffusion equations with discontinuous and spatially variable coefficients. {II:} {The} variable coefficients case},
     journal = {Electronic transactions on numerical analysis},
     pages = {170--186},
     publisher = {mathdoc},
     volume = {40},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2013__40__a17/}
}
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Lemarié, Florian; Debreu, Laurent; Blayo, Eric. Toward an optimized global-in-time Schwarz algorithm for diffusion equations with discontinuous and spatially variable coefficients. II: The variable coefficients case. Electronic transactions on numerical analysis, Tome 40 (2013), pp. 170-186. http://geodesic.mathdoc.fr/item/ETNA_2013__40__a17/