Toward an Optimized Global-in-Time Schwarz Algorithm for Diffusion Equations with Discontinuous and Spatially Variable Coefficients, Part 2: the Variable Coefficients Case

Florian Lemarié 1, * Laurent Debreu 1 Eric Blayo 1
* Corresponding author
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : 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 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 determine analytically 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.
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00661978
Contributor : Florian Lemarié <>
Submitted on : Sunday, January 22, 2012 - 7:02:06 PM
Last modification on : Wednesday, April 11, 2018 - 1:57:55 AM
Long-term archiving on: Monday, November 19, 2012 - 2:12:02 PM

File

Lemarie_ETNA2_2011.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00661978, version 1

Collections

Citation

Florian Lemarié, Laurent Debreu, Eric Blayo. Toward an Optimized Global-in-Time Schwarz Algorithm for Diffusion Equations with Discontinuous and Spatially Variable Coefficients, Part 2: the Variable Coefficients Case. Electronic Transactions on Numerical Analysis, Kent State University Library, 2013, 40, pp.170-186. ⟨hal-00661978⟩

Share

Metrics

Record views

772

Files downloads

266