Many processes in engineering as well as in the natural and life sciences are described by time-dependent differential equations. Our goal is to provide efficient and robust numerical solvers that enable the accurate solution of the discretized equations.
Many of the discretized problems have an inherent tensor-structure that allows us to employ low-rank methods. We here develop state of the art techniques that enable an efficient treatment of such problems.
Employing a monolithic approach representing "all of the physics" and "all-of-the optimization" in one system, we often require many time-steps and are led to large-scale problems. We here combine modern HPC techniques with state-of-the-art algorithms.
Many problems in material science, image processing or chemistry are well represented using phase-field equations. We here investigate schemes that enable the fast solution by also being robust to parameter changes.
Processes across the sciences are described by differential equations and we here consider their discretized counterparts and provide accelrated methods for obtaining an accurate solution to such problems.