Discontinuous Coarse Spaces for DD-Methods with Discontinuous Iterates

Gander, Martin J.; Halpern, Laurence; Repiquet, Kévin Santugini

doi:10.1007/978-3-319-05789-7_58

Cited by 11 publications

(12 citation statements)

References 15 publications

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“…In this section, we recall the formulation of Optimized Schwarz Methods, the ideas behind the use of Discontinuous Coarse Spaces (DCS), and the DCS-DMNV [10] algorithm.…”

Section: Optimized Schwarz Methods and Discontinuous Coarse Spacesmentioning

confidence: 99%

“…Such a coarse space should contain discontinuous functions. The motivations behind the use of discontinuous coarse spaces can be found in details in [10]. The basic idea is that since many DDM, and in particular Opimized Schwarz Methods (OSM), introduce discontinuities at the interfaces between subdomains, we need coarse functions with discontinuities also located at the interface between subdomains to compensate those discontinuities.…”

Section: Optimized Schwarz Methods and Discontinuous Coarse Spacesmentioning

confidence: 99%

See 1 more Smart Citation

A Discontinuous Galerkin like Coarse Space correction for Domain Decomposition Methods with continuous local spaces: the DCS-DGLC Algorithm

Santugini

2014

ESAIM: ProcS

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Abstract. In this paper, we are interested in scalable Domain Decomposition Methods (DDM). To this end, we introduce and study a new Coarse Space Correction algorithm for Optimized Schwarz Methods(OSM): the DCS-DGLC algorithm. The main idea is to use a Discontinuous Galerkin like formulation to compute a discontinuous coarse space correction. While the local spaces remain continuous, the coarse space should be discontinuous to compensate the discontinuities introduced by the OSM at the interface between neighboring subdomains. The discontinuous coarse correction algorithm can be used not only with OSM but also with any one-level DDM that produce discontinuous iterates. While ideas from Discontinuous Galerkin(DG) are used in the computation of the coarse correction, the final aim of the DCS-DGLC algorithm is to compute in parallel the discrete solution to the classical non-DG finite element problem. Résumé. Dans cet article, nous nous intéressons aux Méthods de Décomposition de Domaines (DDM)scalables.À cette fin, nous introduisons etétudions un nouvel algorithme, le DCS-DGLC, de correction grossière pour les méthodes de Schwarz optimisées. L'idée principale est d'utiliser une formulation apparentée aux méthodes de Galerkin discontinues pour calculer une correction grossière discontinue. Alors même que les espaces locaux restent continus, l'espace grossier est choisi discontinu afin de pouvoir compenser les discontinuités introduites par les OSM aux interfaces entre sous-domaines voisins. Cet algorithme de correction grossière discontinue peutêtre employé non seulement avec les OSM mais aussi avec toute DDM de un niveau qui produit des itérées discontinues. Bien que l'algorithme s'inspire des méthodes de Galerkin discontinues, le but final de l'agorithme est de calculer en parallèle la solution discreteà la formulationéléments finis classique, sans DG.

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“…In this section, we recall the formulation of Optimized Schwarz Methods, the ideas behind the use of Discontinuous Coarse Spaces (DCS), and the DCS-DMNV [10] algorithm.…”

Section: Optimized Schwarz Methods and Discontinuous Coarse Spacesmentioning

confidence: 99%

Section: Optimized Schwarz Methods and Discontinuous Coarse Spacesmentioning

confidence: 99%

A Discontinuous Galerkin like Coarse Space correction for Domain Decomposition Methods with continuous local spaces: the DCS-DGLC Algorithm

Santugini

2014

ESAIM: ProcS

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“…Notice that the dimension of V N c is proportional to N . It is clear that the coarse space V N c has mainly information condensed on the boundaries of the objects, similar to the Spectral Harmonically Enriched Multiscale coarse space SHEM in domain decomposition [21,20], which contains mainly information on the interfaces between subdomains, see also [19,18]. It is important to remark that the construction of each function ϕ j,n would require the solution of problem (6.1), which requires the same computational effort of the original problem (2.3).…”

Section: Scalability Analysis and Coarse Correctionmentioning

confidence: 99%

Methods of Reflections: relations with Schwarz methods and classical stationary iterations, scalability and preconditioning.

Ciaramella¹,

Gander²,

Halpern³

et al. 2019

The SMAI Journal of Computational Mathematics

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“…A separate optimal coarse space was developed in Gander and Halpern (2012), and also introduced in Gander et al (2014b), with easy to use approximations to get practical coarse spaces, see also Gander et al (2014a) where the case of discontinuous subdomain iterates was treated. Coarse spaces can however do much more for a subdomain iteration than just make it scalable.…”

Section: Part IIImentioning

confidence: 99%