Matrix-Free Geometric Multigrid Preconditioning Of Combined Newton-GMRES For Solving Phase-Field Fracture With Local Mesh Refinement

TL;DR

This paper presents a matrix-free geometric multigrid preconditioning approach combined with Newton-GMRES for efficiently solving phase-field fracture problems with local mesh refinement, improving computational performance.

Contribution

It introduces a novel matrix-free geometric multigrid preconditioner integrated with Newton-GMRES for phase-field fracture simulations on locally refined meshes.

Findings

Effective solver demonstrated on locally refined meshes

Improved convergence with matrix-free multigrid preconditioning

Applicable to quasi-static phase-field fracture problems

Abstract

In this work, the matrix-free solution of quasi-static phase-field fracture problems is further investigated. More specifically, we consider a quasi-monolithic formulation in which the irreversibility constraint is imposed with a primal-dual active set method. The resulting nonlinear problem is solved with a line-search assisted Newton method. Therein, the arising linear equation systems are solved with a generalized minimal residual method (GMRES), which is preconditioned with a matrix-free geometric multigrid method including geometric local mesh refinement. Our solver is substantiated with a numerical test on locally refined meshes.