Parallel Matrix-Free Higher-Order Finite Element Solvers for Phase-Field Fracture Problems

Autor:	Daniel Jodlbauer, Ulrich Langer, Thomas Wick
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	phase-field fracture propagation low- and higher-order finite element discretization matrix-free solvers geometric multigrid preconditioners parallelization Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939 Electronic computers. Computer science QA75.5-76.95
Zdroj:	Mathematical and Computational Applications, Vol 25, Iss 3, p 40 (2020)
Druh dokumentu:	article
ISSN:	2297-8747 1300-686X
DOI:	10.3390/mca25030040
Popis:	Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with Galerkin finite elements and primal-dual active set methods. Specifically, low-order and high-order finite elements may be employed, where, for the latter, only few studies exist to date. The most time-consuming part in the discrete version of the primal-dual active set (semi-smooth Newton) algorithm consists in the solutions of changing linear systems arising at each semi-smooth Newton step. We propose a new parallel matrix-free monolithic multigrid preconditioner for these systems. We provide two numerical tests, and discuss the performance of the parallel solver proposed in the paper. Furthermore, we compare our new preconditioner with a block-AMG preconditioner available in the literature.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/f469ba7d732c435981fe4e289057fe61 Zobrazit plný text záznamu View record in DOAJ