Updating strategy of a domain decomposition preconditioner for parallel solution of dynamic fracture problems

Abstract Iterative methods used for analysis of multiphysics problems that result in localized solution features may be highly demanding from a computational standpoint and often require special treatment to be more efficient. Dynamic fracture of metals is one such example in which a nonlinear thermo-mechanical system leads to strain localization, resulting in shear bands and/or cracks, in which iterative solvers may have difficult time converging. In the current paper, we develop a novel updating domain decomposition preconditioner for parallel solution of dynamic fracture problems, in which shearbands are modeled using a temperature-dependent viscoplastic material model and fracture is modeled by the phase-field method. The domain decomposition method is based on the Additive Schwarz Method (ASM). The key idea is to decompose the computational domain into two subdomains, a localized subdomain that includes all localized features of the solution and a healthy subdomain for the remaining part of the domain. In this way, one can apply different solvers in each subdomain, i.e. focus more effort in the localized subdomain. In this work, an LU solver is applied in both subdomains, however, while the localized subdomain is solved exactly at every nonlinear iteration, the healthy subdomain LU operator is reused and only selectively updated. Hence, significant CPU time savings associated with the setup of the preconditioner can be achieved. To this end, we propose a strategy for updating the preconditioner in the healthy subdomain. The strategy is based on an idealized performance-based optimization procedure that takes into account machine on-the-fly execution time. Three dynamic fracture problems corresponding to different failure modes are investigated. Excellent performance of the proposed updating preconditioner is reported in serial and parallel computers.