Block preconditioning strategies for generalized continuum models with micropolar and nonlocal damage formulations

Abstract

AbstractIn this work, preconditioning strategies are developed in the context of generalized continuum formulations used to regularize multifield models for simulating localized failure of quasi‐brittle materials. Specifically, a micropolar continuum extended by a nonlocal damage formulation is considered for regularizing both, shear dominated failure and tensile cracking. For such models, additional microrotation and nonlocal damage fields, and their interactions, increase the complexity and size of the arising linear systems. This increases the demand for specialized preconditioning strategies when iterative solvers are adopted. Herein, a block preconditioning strategy, employing algebraic multigrid methods (AMG) for approximating the application of sub‐block inverses, is developed and tested in three steps. First, a block preconditioner is introduced for linear systems resulting from micropolar models. For this case, a simple sparse Schur complement approximation, which is practical to compute, is proposed and analyzed. It is tested for three different discretizations. Second, the developed preconditioner is extended to reflect the additional nonlocal damage field. This extended three‐field preconditioner is tested on the simulation of a compression test on a sandstone sample. All numerical tests show an improved performance of the block preconditioning approach in comparison to a black‐box monolithic AMG approach. Finally, a problem‐adapted preconditioner setup strategy is proposed, which involves a reuse of the multigrid hierarchy during nonlinear iterations, and additionally accounts for the different stages occurring in the simulation of localized failure. The problem‐adapted preconditioning strategy has the potential to further reduce the total computation time.