Solving Phase-Field Fracture with LBFGS and Matrix-Free Geometric Multigrid Preconditioning on Locally Refined Meshes
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In this presentation, the solution of quasi-static phase-field fracture problems is further investigated. The resulting non-convex and nonlinear problem is solved with a L-BFGS method. Therein, the arising linear equation systems are solved with FGMRES, preconditioned with a matrix-free geometric multigrid method. To account for changing constraints resulting from the irreversibility condition, the preconditioner is split and uses local smoothing as well as global coarsening. Our solver is substantiated with numerical tests on locally refined meshes through experiments involving brittle and quasi-brittle fracture scenario.
