The development of adequate numerical models for environmental phenomena is challenging because they typically involve strongly coupled systems of processes from several scientific disciplines. A deep understanding of these processes, a solid knowledge of applied mathematics, and the use of new hardware and software technologies on large HPC systems are required to achieve improvements and gain new insights.

The EMCL contributes to interdisciplinary projects by providing research contributions at different stages of the numerical simulation – from the mathematical modelling of a physical phenomenon, to its hardware-optimised implementation, from pre-processing, to post-processing and analysis. Due to the high complexity, the multi-scale structure and the high degree of coupling, problem-specific solution methods are required. Therefore, existing numerical methods are extended or new ones are developed that can be efficiently used on large computer systems and new architectures to achieve the required accuracy. We consider, among others the following methods:

•  Adaptivity in space and time (e.g. error estimators, space-time finite elements);
• Model reduction (e.g. proper orthogonal decomposition, model adaptivity);
• Operator splitting, domain decomposition;
• Problem adapted solvers (e.g. preconditioning, efficient time stepping);
• Hardware-aware numerics (e.g. in the context of parareal time integration).