The development of adequate numerical models for environmental phenomena is challenging since these are typically related to strongly coupled systems of processes from several scientific disciplines. Deep understanding of these processes, solid knowledge in applied mathematics, and deployment of new hard- and software technologies on large HPC systems are required to achieve improvements and gain new insights.

The EMCL contributes to interdisciplinary projects by assistance on various stages of the numerical simulation – from the mathematical modeling of a physical phenomenon, to its hardware-depending optimized implementation, over preprocessing, to postprocessing issues and finally also analysis. Due to the high complexity, multi-scale structure and high degree of coupling, most often problem-dependent solution procedures are required. Therefore, existing numerical methods are extended or new ones are developed that can efficiently be used on large computer systems and new architectures to achieve the required precision. Amongst others, we consider the following methodologies

• 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).

To address such interdisciplinary scientific questions, a strong cooperation between the EMCL and partners from the different scientific disciplines is given in all projects.