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UID:5904@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20221023T000000
DTEND;TZID=Europe/Paris:20221028T000000
DTSTAMP:20241120T200652Z
URL:https://www.i2m.univ-amu.fr/evenements/optimized-discrete-schwarz-meth
 ods-for-anisotropic-elliptic-problems-morlet-chair-martin-gander/
SUMMARY:Pairs (CIRM\, Luminy\, Marseille): Optimized Discrete Schwarz Metho
 ds for Anisotropic Elliptic Problems (Morlet Chair - Martin Gander)
DESCRIPTION:Pairs: \n\n\n\n\n\n\n\nCIRM - Jean-Morlet Chair \n Martin GANDE
 R &amp\; Florence HUBERT\n\nNumerical Methods for PDEs: Discretization\, I
 terative Solution and Parallelization\n\nMéthodes numériques pour les ED
 P: discrétisation\, solution itérative et parallélisation\n\n\n 2022 - 
 semester 2\n\n\n\n\n\n\n\n\n\n\n\n\nRESEARCH IN PAIRS\nOptimized Discrete 
 Schwarz Methods for Anisotropic Elliptic Problems \n​Date: 23-28 octobre
  2022\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nDESCRIPTION\nThis research in pairs foc
 uses on the development and the understanding of optimized discrete Schwar
 z methods based on the Discrete Duality Finite Volume (DDFV for short) dis
 cretization for anisotropic elliptic problems. The collaboration\, based o
 n the expertise of Martin Gander and Laurence Halpern on domain decomposit
 ion methods and of Florence Hubert and Stella Krell on DDFV methods\, star
 ted about ten years ago.\nSchwarz algorithms are a well-known strategy to 
 solve problems on large domains iteratively\, and they are often used at t
 he discrete level as pre-conditioners for large linear systems [8\, 3]. DD
 FV methods have been developed in the late 90’s [2\, 1] to approximate l
 inear and nonlinear elliptic problems on general meshes. The good properti
 es of DDFV have extensively been tested in the benchmark [7]. Combining DD
 FV with Schwarz methods enabled us to propose new discrete algorithms for 
 elliptic problems [6\, 4]. We are focusing on Robin and Ventcell transmiss
 ion conditions for non-overlapping Schwarz methods\, on proving convergenc
 e of the algorithm\, on the optimization of the transmission parameters\, 
 and comparing optimal parameters obtained for the continuous problem to th
 e ones for the discrete problem on uniform grids and for the discrete prob
 lem on general grids [5].\n​This research in pairs will enable us to com
 plete our work including the hard problem of cross points (intersection of
  at least three domains)\, and to work on overlapping discrete Schwarz met
 hods for anisotropic elliptic problems.\n\n\n \n\nPARTICIPANTS\n\n\n 	Mar
 tin Gander (Université de Genève &amp\; Aix-Marseille Université)​\n 
 	Laurence Halpern (Université Sorbonne Paris Nord)\n 	Florence Hubert (Ai
 x-Marseille Université)\n 	Stella Krell (Université Côte d'Azur)\n\n\n\
 nREFERENCES\n\n\n[1] B. Andreianov\, F. Boyer\, and F. Hubert. Discrete du
 ality finite volume schemes for Leray-Lions type elliptic problems on gene
 ral 2D-meshes. Num. Meth. for PDEs\, 23(1):145–195\, 2007.\n\n[2] K. Dom
 elevo and P. Omnes. A finite volume method for the Laplace equation on alm
 ost arbitrary two-dimensional grids. M2AN Math. Model. Numer. Anal.\, 39(6
 ):1203–1249\, 2005.\n\n[3] M. J. Gander. Schwarz methods over the course
  of time. Electronic transactions on numerical analysis\, 31:228–255\, 2
 008.\n\n[4] M. J. Gander\, L. Halpern\, F. Hubert\, and S. Krell. DDFV Ven
 tcell Schwarz algorithms. In Domain Decomposition Methods in Science and E
 ngineering XXII\, pages 481–489. Springer\, 2016.\n\n[5] M. J. Gander\, 
 L. Halpern\, F. Hubert\, and S. Krell. Optimized Schwarz methods for aniso
 tropic diffusion with discrete duality finite volume discretizations. subm
 itted\, 2019.\n\n[6] M. J. Gander\, F. Hubert\, and S. Krell. Optimized Sc
 hwarz algorithms in the framework of ddfv schemes. In Domain Decomposition
  Methods in Science and Engineering XXI\, pages 457–466. Springer\, 2014
 .\n\n[7] R. Herbin and F. Hubert. Benchmark on discretization schemes for 
 anisotropic diffusion problems on general grids. In R. Eymard and J.-M. H
 érard\, editors\, Finite Volumes for Complex Applications V\, pages 659
 – 692. John Wiley &amp\; Sons\, 2008.\n\n[8] P. L. Lions. On the Schwarz
  alternating method. III. A variant for non-overlapping subdomains. In Thi
 rd International Symposium on Domain Decomposition Methods for Partial Dif
 ferential Equations (Houston\, TX\, 1989)\, pages 202–223. SIAM\, Philad
 elphia\, PA\, 1990.\n\n\n\n\n\n\n\n\n\nSPONSOR\n\n\n\n\n\n\n\n\n\n\n\n  \n
 \n\n\n\n\n\n\n  \n\n\n\n\n\n\n\n  \n\n\n\n\n\n\n\n  \n\n\n\n\n\n\n\n\n\n\n
 \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 022/03/image_aa-hal-02539124-First-and-third-iteration-of-the-DDFV-optimiz
 ed-Schwarz-method-with-Ventcell-transmission-Florence_Hubert-x350.png
CATEGORIES:Manifestation scientifique,Morlet Research in Pairs
LOCATION:Luminy - CIRM\, 163 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=Luminy - CIRM:geo:0,0
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