A Multi-Time Stepping Algorithm for the Modelling of Heterogeneous Structures With Explicit Time Integration

Abstract

Heterogeneous solids often exhibit complex dynamic behavior, requiring simulations to use varying time steps. However, the conventional use of a single-time step for the entire domain can be inefficient. This article proposes a multi-time stepping algorithm that addresses this challenge by relaxing the constraint for an integer or constant time step ratio between subdomains and eliminating the need for kinematic interpolation. The algorithm ensures the satisfaction of the Courant-Friedrichs-Lewy condition, deviating only to allow subdomains to remain in synchronization. Consequently, less integration steps are performed in comparison to state-of-the-art asynchronous integrators. We extend to the coupling of multiple subdomains, where each subdomain has its time step. Simulating stress wave propagation in metamaterials demonstrates that the proposed algorithm significantly accelerates simulation time, without sacrificing accuracy.