Truncated Nonsmooth Newton Multigrid for phasefield brittlefracture problems
Abstract
We propose the Truncated Nonsmooth Newton Multigrid Method (TNNMG) as a solver for the spatial problems of the smallstrain brittlefracture phasefield equations. TNNMG is a nonsmooth multigrid method that can solve biconvex, blockseparably nonsmooth minimization problems in roughly the time of solving one linear system of equations. It exploits the variational structure inherent in the problem, and handles the pointwise irreversibility constraint on the damage variable directly, without penalization or the introduction of a local history field. Memory consumption is significantly lower compared to approaches based on direct solvers. In the paper we introduce the method and show how it can be applied to several established models of phasefield brittle fracture. We then prove convergence of the solver to a solution of the nonsmooth EulerLagrange equations of the spatial problem for any load and initial iterate. Numerical comparisons to an operatorsplitting algorithm show a speed increase of more than one order of magnitude, without loss of robustness.
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2007.12290
 Bibcode:
 2020arXiv200712290G
 Keywords:

 Mathematics  Numerical Analysis;
 74R05;
 74S05;
 65K15