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

研究领域：数值分析与软件工程在过去的十年中，拉普拉斯和低频亥姆霍兹问题的快速直接求解器的发展取得了巨大的进步。这些是基于底层格林函数的远场相互作用的低秩压缩，并且根据公式，实现对数线性或近对数线性复杂性。与此同时，高性能计算领域已经从纯CPU系统迅速发展到越来越多的异构混合CPU/GPU架构。该项目的目标是开发一套快速算法，针对现代异构架构进行优化，使快速多极方法和快速直接求解器在统一框架内的高效HPC实现能够解决大规模电磁散射问题，这些问题到目前为止对现有方法和实现来说是一个重大挑战。

Research Area: Numerical Analysis and Software EngineeringOver 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.