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Is minimizing the convergence rate a good choice for efficient Optimized Schwarz preconditioning in heterogeneous coupling? The Stokes-Darcy case

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posted on 12.02.2018, 10:50 authored by Marco DiscacciatiMarco Discacciati, Luca Gerardo-Giorda
Optimized Schwarz Methods (OSM) are domain decomposition techniques based on Robin-type interface condition that have became increasingly popular in the last two decades. Ensuring convergence also on non-overlapping decompositions, OSM are naturally advocated for the heterogeneous coupling of multiphysics problems. Classical approaches optimize the coefficients in the Robin condition by minimizing the effective convergence rate of the resulting iterative algorithm. However, when OSM are used as preconditioners for Krylov solvers of the resulting interface problem, such parameter optimization does not necessarily guarantee the fastest convergence. This drawback is already known for homogeneous decomposition, but in the case of heterogeneous decomposition, the poor performance of the classical optimization approach becomes utterly evident. In this paper, we highlight this drawback for the Stokes/Darcy problem and we propose a more effective alternative optimization procedure.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Domain Decomposition Methods in Science and Engineering XXIV

Citation

DISCACCIATI, M. and GERARDO-GIORDA, L., 2018. Is minimizing the convergence rate a good choice for efficient Optimized Schwarz preconditioning in heterogeneous coupling? The Stokes-Darcy case. IN: Bjorstad, P.E. ... et al (eds). Domain Decomposition Methods in Science and Engineering XXIV, Berlin: Springer, pp. 233-241.

Publisher

© Springer

Version

AM (Accepted Manuscript)

Publisher statement

The final authenticated version is available online at https://doi.org/10.1007/978-3-319-93873-8.

Publication date

2019-01-05

Notes

This paper was presented at the twenty-fourth International Domain Decomposition Conference, held in Spitsbergen, Svalbard, Norway, in February 2017.

ISBN

9783319938738

ISSN

1439-7358

Book series

Lecture Notes in Computational Science and Engineering;125

Language

en