@inproceedings{d37ace13773241908dd1ae59f361582e,
title = "Matrix-Free Geometric Multigrid Preconditioning of Combined Newton-GMRES for Solving Phase-Field Fracture with Local Mesh Refinement",
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.",
author = "Kolditz, \{Leon M.\} and Thomas Wick",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.; European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2023, ENUMATH 2023 ; Conference date: 04-09-2023 Through 08-09-2023",
year = "2025",
month = apr,
day = "28",
doi = "10.1007/978-3-031-86169-7\_7",
language = "English",
isbn = "9783031861680",
volume = "154",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "64--74",
editor = "Ad{\'e}lia Sequeira and Ana Silvestre and Valtchev, \{Svilen S.\} and Jo{\~a}o Janela",
booktitle = "Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2 - European Conference, 2023",
address = "Germany",
}