In this work, we – Patrick Staubach (BUW) and Jan Machacek – present an approach to combine the stability of implicit time integration with the efficiency of explicit schemes in a single finite-element model.

The result is a mixed implicit–explicit (IMEX) scheme to efficiently solve complex soil dynamics problems, particularly those with significant stiffness variations. By employing domain decomposition with a mortar contact discretisation, we allow different parts of the computational domain to be treated either implicitly or explicitly. This decomposition is exemplarily shown in the following figure:

The IMEX scheme improves computational efficiency by allowing larger time increments for stiff parts of the system (e.g. a pile), while maintaining accuracy for the less stiff domains (soil). This results in reduced computational time, especially in cases where purely explicit methods would require significantly smaller time steps to remain stable.

Check out the full article here.