Temporal and Spatial Coupling Methods for the Efficient Modelling of Dynamic Solids

This paper presents efficient coupling methods that accurately reduce the computational cost for modelling solids dynamically with finite elements. A multi-time-step integration algorithm is developed to leverage varying time steps throughout a domain. Interfaces between subdomains are resolved explicitly with the continuity of acceleration and tractions. A spatial coupling method is combined with multiple time steps, allowing for meshes that do not necessarily conform at their interfaces. The method avoids solving additional degrees of freedom at these interfaces, with parameter-free coupling operators defined between meshes. A speedup >12× is achieved in comparison to reference single-time-step methods.