Matrix-Free Geometric Multigrid Preconditioning Of Combined Newton-GMRES For Solving Phase-Field Fracture With Local Mesh Refinement
<|reference_start|>Matrix-Free Geometric Multigrid Preconditioning Of Combined Newton-GMRES For Solving Phase-Field Fracture With Local Mesh Refinement: 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.<|reference_end|>
@article{kolditz2024matrix-free,
    title={Matrix-Free Geometric Multigrid Preconditioning Of Combined Newton-GMRES
  For Solving Phase-Field Fracture With Local Mesh Refinement},
    author={Leon Maximilian Kolditz and Thomas Wick},
    journal={arXiv preprint arXiv:2404.03265},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.03265},
    primaryClass={math.NA cs.NA}
}