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

## TL;DR

This paper introduces efficient methods to reduce computational costs when modeling dynamic solids using finite elements.

## Contribution

The novel contribution is a parameter-free coupling method combining multi-time-step and non-conforming mesh integration.

## Key findings

- A multi-time-step integration algorithm reduces computational costs while maintaining accuracy.
- The method achieves a speedup of over 12× compared to traditional single-time-step methods.
- Interfaces between subdomains are resolved without additional degrees of freedom.

## Abstract

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.