Fast direct and multipole solvers for electromagnetic scattering problems on heterogeneous architectures

Research Area: Numerical Analysis and Software Engineering

Over the last decade there has been tremendous advancements in the development of fast direct solvers for Laplace and low-frequency Helmholtz problems. These are based on low-rank compressions of far-field interactions of the underlying Green's function and, depending on the formulation, achieve log-linear or near log-linear complexity. At the same time the HPC landscape has rapidly evolved from pure CPU systems to more and more heterogeneous mixed CPU/GPU architectures. The goal of this project is to develop a collection of fast algorithms, optimized for modern heterogeneous architectures, that allow the efficient HPC implementation of fast multipole methods and fast direct solvers within a unified framework with the aim to solve large-scale electromagnetic scattering problems which until now are a significant challenge for existing methods and implementations.