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The parallel finite element system M++ with integrated multilevel preconditioning and multilevel Monte Carlo methods

Baumgarten, Niklas; Wieners, Christian

Abstract:
We present a parallel data structure for the discretization of partial differential equations which is based on distributed point objects and which enables the flexible, transparent, and efficient realization of conforming, nonconforming, and mixed finite elements. This concepts is realized for elliptic, parabolic and hyperbolic model problems, and sample applications are provided by a tutorial complementing a lecture on scientific computing.
The corresponding open-source software is based on this parallel data structure, and it supports multilevel methods on nested meshes and 2D and 3D as well as in space-time. Here, we present generic results on porous media applications including multilevel preconditioning and multilevel Monte Carlo methods for uncertainty quantification.

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Volltext §
DOI: 10.5445/IR/1000117837
Veröffentlicht am 23.03.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000117837
Verlag KIT, Karlsruhe
Umfang 27 S.
Serie CRC 1173 ; 2020/9
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter finite elements, parallel numerical methods, multilevel preconditioner, multilevel Monte Carlo methods
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