Next Article in Journal
ssMousetrack—Analysing Computerized Tracking Data via Bayesian State-Space Models in R
Next Article in Special Issue
How Europe Is Preparing Its Core Solution for Exascale Machines and a Global, Sovereign, Advanced Computing Platform
Previous Article in Journal
Windowing as a Sub-Sampling Method for Distributed Data Mining
Previous Article in Special Issue
CyVerse Austria—A Local, Collaborative Cyberinfrastructure
Open AccessFeature PaperArticle

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. View Full-Text
Keywords: phase-field fracture propagation; low- and higher-order finite element discretization; matrix-free solvers; geometric multigrid preconditioners; parallelization phase-field fracture propagation; low- and higher-order finite element discretization; matrix-free solvers; geometric multigrid preconditioners; parallelization
Show Figures

Figure 1

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 Style

Jodlbauer, 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

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop