The project „PDExa: Optimized software methods for solving partial differential equations on exascale supercomputers“ is funded by BMBF through the initiative SCALEXA. The new class of exascale computing systems currently built or designed offers new opportunities in the numerical simulation supporting science and engineering. In order to utilize the full capabilities of new hardware, new software paradigms need to be developed. These paradigms need to be adapted to the characteristics of the hardware, in particular in terms of compute capabilities and data locality. The project PDExa strives to develop new classes of algorithms and implementations for the efficient distributed solution of partial differential equations with continuous and discontinuous finite element methods in a broad variety of applications. The development is driven by a team of five PIs at five sites, which contribute to the open-source software projects deal.II and Ginkgo as well as the application code ExaDG.

If you hold a Ph.D. or M.Sc. degree in numerical analysis, high-performance computing, numerical linear algebra, PDE solvers, computational mechanics, optimization, or related subjects, we are looking forward to your application to one or several of the positions listed below.

The research focus of the team at the Ruhr University Bochum is on algorithms of mixed precision, focusing on the solution of time-dependent hyperbolic systems with implicit time stepping methods. The research program aims to make these methods more efficient by adddressing the two main bottlenecks of current large-scale parallel computers. On the one hand, the strong scaling limit is influenced by the communication frequency, which is addressed by the development of robust preconditioners for implicit time stepping. On the other hand, many algorithms are limited by memory bandwidth, a limit that can be relaxed by reducing the precision of stored data and hence data transfer. The research project aims to devise mathematically supported algorithms that do not affect the overall efficiency, yet improve the throughput.

See here for details on how to apply

Project PI: Prof. Dr. Katharina Kormann

The research project at the University of Augsburg aims to develop high-performance abstractions for matrix-free finite-element algorithms. The core algorithm is the operator evaluation, which computes the underlying finite-element integrals on the fly. While this might increase the operation counts over classical matrix-based finite element solvers, it drastically reduces the memory transfer, and hence provides speed-ups on modern hardware with high arithmetic capabilities relative to available memory bandwidth. In this research project, the algorithms are extended to meshes with mixed element types and non-conforming elements of the full de-Rham complex, optimized implementations for GPUs and CPUs with SIMD vectorizations will be developed and integrated into optimized iterative solvers, including multigrid solvers and preconditioners of Schwarz type with batched solvers, developed in collaboration with the partners at RUB and KIT. The software will be contributed as general-purpose facilities to the deal.II library and based on abstractions that are developed together with the team TUM-CS.

Apply via e-mail to Prof. Dr. Martin Kronbichler, see the official announcement for the position (in German) here

Project PI: Prof. Dr. Martin Kronbichler

The research project at the Department of Computer Engineering at Technical University of Munich works on performance evaluation and development of novel parallel programming abstractions for the high-order finite element algorithms developed in the other groups. These abstractions target a variety of exascale computer architectures, covering both throughput-oriented architectures (GPUs) as well as latency-sensitive parts in algorithms that are (on today's systems) better addressed by CPU hardware.

Project PI: Prof. Dr. rer. nat. Martin Schulz