Prof. Dr. Christian Engwer, Angewandte Mathematik Münster: Institut für Analysis und Numerik

Numerical methods for solving partial differential equations (PDE) are of central importance in many fields of application. Constantly increasing model details require almost unlimited computer power. To use modern hardware efficiently new dedicated numerical methods are necessary. Special challenges are posed by the increasing parallelism, especially the instruction level parallelism, as well as the ever increasing gap between memory and computing speed. The aim of this proposal is improve the hardware efficiency of a broad class of numerical methods for instationary PDEs. By developing modern numerical methods under the constraints posed by current hardware, we will provide approaches which are easily applicable to existing simulation codes. The numerical approach is based on preliminary work on block-Krylov methods. Combining them with parallel-in-time methods facilitates the transparent use of vector units of modern CPUs and by this allows to utilize a significant portion of the attainable peak performance. The approach allows for a speedup that would otherwise not be possible for classical low-order methods and does furthermore increase the local problem size, contributing to an improved strong-scaling. We will contribute to an improved hardware efficiency by development of new numerical methods, analysis of their performance, a hardware-efficient implementation and its validation.