Preconditioning strategies for vectorial finite element linear systems arising from phase-field models for fracture mechanics

Phase-field models are frequently adopted to simulate fracture mechanics problems in the context of finite element method. To depict fracture, this method involves solving a coupled set Helmholtz-like damage-field equation and augmented linear momentum balance equation. Solutions these equations then used as descriptions crack propagation phenomena within solids. However, imposes constrain using extremely fine meshing for properly predicting cracks. For practical interest, very often leads systems with large sizes that have be repetitively assembled solved. As such, iterative solution procedures such Krylov subspace-based methods framework serial/parallel computing environments become mandatory obtain results feasible time. In work, vectorial discretization hybrid phase-field formulation – monolithic scheme is presented. The underlying nonlinearity present model dealt through Picard iteration helps preserve symmetry linearized system solve. Due symmetric positive definite nature obtained problem, conjugate gradient makes standard choice algorithm. article, improve convergence rates, consequently time solution, applied problems, different preconditioning strategies analyzed, tuned, discussed. Brittle benchmarks measure performance preconditioners which massively parallel simulations millions unknowns. A series numerical experiments show algebraic multigrid preconditioner well suited being superior Jacobi block all regards: ease iterations converge, scaling on more than thousand processes.