Abstract
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.
Highlights
Many applications require the solution of partial differential equations (PDEs)
These are solved by Finite Element Methods (FEM), or related approaches like Isogeometric Analysis, which discretize the continuous PDE
We focus on efficient parallel solvers for problems in phase-field fracture (PFF) propagation
Summary
Many applications require the solution of partial differential equations (PDEs). These are solved by Finite Element Methods (FEM), or related approaches like Isogeometric Analysis, which discretize the continuous PDE. We eventually need to solve huge linear systems of equations. This may become a challenging task since the computational effort increases rapidly. Solvers that are able to handle large-scale linear systems are required. This gives rise to specialized solvers, that are adapted towards a specific PDE. We focus on efficient parallel solvers for problems in phase-field fracture (PFF) propagation
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