A Low-Communication FDFD Solver for Distributed Parallel Electromagnetic Simulation

This paper presents a low-communication finite-difference frequency-domain (LC-FDFD) solver for distributed parallel simulation of large-scale three-dimensional scattering problems. We propose a customized matrix reordering scheme that preserves spatial locality of field components and transforms the FDFD system into a compact banded structure. Based on the reordering scheme, a hybrid iterative-direct solver based on the SPIKE algorithm is proposed to partition the global system into independent subproblems solvable in parallel across multiple GPUs in a distributed cluster. When solving reordered FDFD systems with wide bandwidth and in-band sparsity, the proposed method avoids explicit spike matrix construction by using a matrix-free technique, thereby significantly reducing both computational cost and memory requirements. Several numerical experiments are presented, whose results show excellent efficiency and scalability for large-scale electromagnetic simulations.