Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Wasiak, Adam (2021). Adaptive and Frugal FETI-DP for Virtual Elements. Technical Report.

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Abstract

The FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) method has recently successfully been applied to virtual element discretizations, adding more flexibility to the resolution of possibly complicated underlying domain geometries. However, for second-order partial differential equations with large discontinuities in the coefficient functions, in general, the convergence rate of domain decomposition methods is known to deteriorate if the coarse space is not properly adjusted. For finite element discretizations, this problem can be solved by using adaptive coarse spaces, which guarantee a robust method for arbitrary coefficient distributions, or by the computationally much cheaper frugal coarse space, which numerically proved to be robust for many realistic coefficient distributions. In this article, both, the adaptive and the frugal FETI-DP methods are applied to discretizations obtained by using virtual elements. As model problems, stationary diffusion and compressible linear lasticity in two spatial dimensions are considered. The performance of the methods is numerically tested, varying the quasi-uniformity of the underlying meshes, the polynomial degree, the scaling method, and considering regular and irregular domain decompositions. It is shown that adaptive and frugal FETI-DP for virtual elements behave similarly as in the finite element case.

Item Type:	Monograph (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Klawonn, Axel axel.klawonn@uni-koeln.de https://orcid.org/0000-0003-4765-7387 UNSPECIFIED Lanser, Martin martin.lanser@uni-koeln.de https://orcid.org/0000-0002-4232-9395 UNSPECIFIED Wasiak, Adam adam.wasiak@uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-539792
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2021-10
Date:	11 November 2021
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Center for Data and Simulation Science
Subjects:	Natural sciences and mathematics Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language virtual elements English FETI-DP English domain decomposition methods English robust coarse spaces English adaptive coarse spaces English
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/53979