Efficient Heterogeneous Scalable Finite Element Exterior Calculus Simulations for Electromagnetic Scattering on Manifold

When it comes to complex electromagnetic phenomena, modern heterogeneous supercomputers provide a powerful tool. For effective implementation of simulations on these platforms, computational electrodynamics algorithms need to exhibit good stability, long-term conservation, unstructured modeling capability, and large-scale scalability. Inspired by differential geometry theory, the Finite Element Method (FEM), and the Finite-Difference Time-Domain (FDTD) algorithm, the Scalable Finite Element Exterior Calculus (SFEEC) scheme developed for Maxwell’s equations has proven to be an advanced numerical tool. It combines the efficiency, stability, conservation, and scalability of FDTD with the unstructured modeling capability and high-order precision of FEM. Multi-level heterogeneous codes, designed and constructed via the HIP and MPI frameworks, show excellent adaptability to C86 CPUs and DCUs. Strategies such as task topology-oriented communication optimization and overlapping computation techniques were employed to achieve a good load balance and significant parallel efficiency. Numerical experiments performed on the ‘Songshan’ supercomputer have effectively demonstrated the computational efficiency and performance of the SFEEC scheme. The algorithm and codes were carefully verified via the Mie scattering problem. A systematic study of specific mesoscopic metal particle array scattering phenomena provided a relatively complete physical picture of plasmonic scattering. The heterogeneous simulation framework established in this work demonstrates substantial potential for application in complex electromagnetics, contributing significantly to the field of computational electromagnetics.