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Matrix-Free Geometric Multigrid Preconditioning Of Combined Newton-GMRES For Solving Phase-Field Fracture With Local Mesh Refinement (2404.03265v2)

Published 4 Apr 2024 in math.NA and cs.NA

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.

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