Scalable, recursively configurable, massively-parallel FEM-multigrid solvers for heterogeneous hardware architectures -- Design, analysis and realisation in FEAST with applications in fluid mechanics

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This joint project examines numerical methods for massively-parallel multigrid methods for finite element discretisations of variable order. Special emphasis is placed on techniques that enable robustness and uniform scalability on modern heterogeneous hardware architectures, in particular on hybrid systems comprising conventional CPU-like processors combined with throughput-optimised accelerator designs like graphics processors (GPUs). The goal of uniform scalability is very challenging and embraces aspects of numerical scalability (convergence rates independent of problem size and problem partitioning), the minimisation or even avoidance of sequential components on all parallelism layers of hybrid systems, the equal degree of utilisation of all compute resources, and the numerically stable and robust asynchronous and fault-tolerant parallel execution. In addition, novel numerical methods along with suitable implementation techniques are developed and analysed (hardware-oriented numerics), so that efficient -- simultaneously wrt. numerics, parallelism and hardware -- discretisation and solution techniques can be provided for a broad range of flow problems. Joint work in this research project is incorporated both in independently usable libraries as well as the common FEAST software package that has been developed intinsively during the last years, so that a numerically robust, scalable and recursively configurable methodology for massively-parallel multigrid methods on heterogeneous hardware platforms can be realised and analysed.