Parallel Matrix-Free Higher-Order Finite Element Solvers for Phase-Field Fracture Problems
1
Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Straße 69, 4040 Linz, Austria
2
Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2020, 25(3), 40; https://doi.org/10.3390/mca25030040
Received: 27 May 2020 / Revised: 2 July 2020 / Accepted: 3 July 2020 / Published: 7 July 2020
(This article belongs to the Special Issue High-Performance Computing 2020)
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.
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Keywords:
phase-field fracture propagation; low- and higher-order finite element discretization; matrix-free solvers; geometric multigrid preconditioners; parallelization
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MDPI and ACS Style
Jodlbauer, D.; Langer, U.; Wick, T. Parallel Matrix-Free Higher-Order Finite Element Solvers for Phase-Field Fracture Problems. Math. Comput. Appl. 2020, 25, 40. https://doi.org/10.3390/mca25030040
AMA Style
Jodlbauer D, Langer U, Wick T. Parallel Matrix-Free Higher-Order Finite Element Solvers for Phase-Field Fracture Problems. Mathematical and Computational Applications. 2020; 25(3):40. https://doi.org/10.3390/mca25030040
Chicago/Turabian StyleJodlbauer, Daniel; Langer, Ulrich; Wick, Thomas. 2020. "Parallel Matrix-Free Higher-Order Finite Element Solvers for Phase-Field Fracture Problems" Math. Comput. Appl. 25, no. 3: 40. https://doi.org/10.3390/mca25030040
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