Geodesic
Toward an optimized global-in-time Schwarz algorithm for diffusion equations with discontinuous and spatially variable coefficients. I: The constant coefficients case
Electronic transactions on numerical analysis, Tome 40 (2013), pp. 148-169
In this paper we present a global-in-time non-overlapping Schwarz method applied to the one-dimensional unsteady diffusion equation. We address specifically the problem with discontinuous diffusion coefficients, our approach is therefore especially designed for subdomains with heterogeneous properties. We derive efficient interface conditions by solving analytically the minmax problem associated with the search for optimized conditions in a $Robin-Neumann$ case and in a two-sided Robin-Robin case. The performance of the proposed schemes are illustrated by numerical experiments.
Classification : 65M55, 65F10, 65N22, 35K15
Keywords: optimized Schwarz methods, waveform relaxation, alternating and parallel Schwarz methods 
@article{ETNA_2013__40__a18,
     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. {I:} {The} constant coefficients case},
     journal = {Electronic transactions on numerical analysis},
     pages = {148--169},
     year = {2013},
     volume = {40},
     zbl = {1288.65137},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2013__40__a18/}
}
TY  - JOUR
AU  - Lemarié,  Florian
AU  - Debreu,  Laurent
AU  - Blayo,  Eric
TI  - Toward an optimized global-in-time Schwarz algorithm for diffusion equations with discontinuous and spatially variable coefficients. I: The constant coefficients case
JO  - Electronic transactions on numerical analysis
PY  - 2013
SP  - 148
EP  - 169
VL  - 40
UR  - http://geodesic.mathdoc.fr/item/ETNA_2013__40__a18/
LA  - en
ID  - ETNA_2013__40__a18
ER  - 
%0 Journal Article
%A Lemarié,  Florian
%A Debreu,  Laurent
%A Blayo,  Eric
%T Toward an optimized global-in-time Schwarz algorithm for diffusion equations with discontinuous and spatially variable coefficients. I: The constant coefficients case
%J Electronic transactions on numerical analysis
%D 2013
%P 148-169
%V 40
%U http://geodesic.mathdoc.fr/item/ETNA_2013__40__a18/
%G en
%F ETNA_2013__40__a18
Lemarié,  Florian; Debreu,  Laurent; Blayo,  Eric. Toward an optimized global-in-time Schwarz algorithm for diffusion equations with discontinuous and spatially variable coefficients. I: The constant coefficients case. Electronic transactions on numerical analysis, Tome 40 (2013), pp. 148-169. http://geodesic.mathdoc.fr/item/ETNA_2013__40__a18/