Adaptive and Frugal FETI-DP for Virtual Elements - Kölner UniversitätsPublikationsServer

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin ORCID: 0000-0002-4232-9395 and Wasiak, Adam ORCID: 0000-0002-5705-9754 (2023). Adaptive and Frugal FETI-DP for Virtual Elements. Vietnam J. Math., 51 (1). S. 89 - 112. SINGAPORE: SPRINGER SINGAPORE PTE LTD. ISSN 2305-2228

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DOI:10.1007/s10013-022-00580-5

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 elasticity 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:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Klawonn, Axel	UNSPECIFIED	orcid.org/0000-0003-4765-7387	UNSPECIFIED
Lanser, Martin	UNSPECIFIED	orcid.org/0000-0002-4232-9395	UNSPECIFIED
Wasiak, Adam	UNSPECIFIED	orcid.org/0000-0002-5705-9754	UNSPECIFIED