Parallel Computing with the Thick Level Set Method

The thick level set (TLS) method has been proposed as a nonlocal damage model for the modeling of failure in solids being able to deal with crack initiation, branching, and merging. The nonlocality of the TLS is achieved by introducing a characteristic length into the problem. This way, the TLS does not suffer from spurious localization in the strain field. This paper introduces a domain decomposition method to obtain a parallel implementation of the TLS method. It describes how to handle the numerical features specific to the TLS analysis steps involving level set update, equilibrium solution, and damage front advance. For each of these tasks an appropriate parallel strategy is proposed. The most demanding task in terms of computational cost, i.e., solving the linearized system of equations from the equilibrium problem, is performed with a parallel iterative method profiting from the domain decomposition method adopted. A communication strategy to deal with enriched nodes belonging to shared regions of subdomains is provided. Collective communication strategies are also proposed to deal with operations related to the level set update and damage front advance. Numerical experiments demonstrate the accuracy and efficiency of the proposed framework to handle parallel computing with the TLS method.