27th Conference of the International Linear Algebra Society (ILAS 2026)

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

May 18, 2026, 4:10 PM

25m

Goodwin Hall 155 (Virginia Tech)

Minisymposium Talk Application-Driven Family of Matrix Computations: Factorization, Inverse, Linear Solve Application-Driven Family of Matrix Computations: Factorization, Inverse, Linear Solve

Speaker

Prof. Thomas Wick (Leibniz University Hannover)

Description

In this talk, 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. Afterwards, we discuss applications of this solver framework in fluid-filled fractures in porous media.