Solving very large scattering problems using a parallel PWTD-enhanced surface integral equation solver

Summary form only given. The computational complexity and memory requirements of multilevel plane wave time domain (PWTD)-accelerated marching-on-in-time (MOT)-based surface integral equation (SIE) solvers scale as O(N_tN_s(log²)N_s) and O(N_s^1.5); here N_t and N_s denote numbers of temporal and spatial basis functions discretizing the current [Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003]. In the past, serial versions of these solvers have been successfully applied to the analysis of scattering from perfect electrically conducting as well as homogeneous penetrable targets involving up to N_s ≈ 0.5 × 10⁶ and N_t ≈ 10³. To solve larger problems, parallel PWTD-enhanced MOT solvers are called for. Even though a simple parallelization strategy was demonstrated in the context of electromagnetic compatibility analysis [M. Lu et al., in Proc. IEEE Int. Symp. AP-S, 4, 4212-4215, 2004], by and large, progress in this area has been slow. The lack of progress can be attributed wholesale to difficulties associated with the construction of a scalable PWTD kernel. Recently, we developed a new parallel PWTD kernel that leverages an advanced hierarchical and provably scalable spatial, angular, and temporal load partitioning strategy [Y. Liu et. al., in URSI Digest, 2012]. Here, we adopt this new PWTD kernel to solve time domain electric, magnetic, and combined field SIEs pertinent to the analysis of scattering from perfect electrically conducting objects; all SIEs are discretized using standard RWG spatial basis and testing functions, and shifted Lagrange temporal interpolators. Just like in parallel frequency domain FMM-accelerated SIE solvers, “far-fields” are evaluated using the parallel PWTD scheme; classical “near-field” computations and the actual MOT operation also are performed- in parallel. The interplay between the PWTD and classical code components calls for CPU versus memory trade-offs that are quite different from those encountered in frequency-domain FMM-accelerated SIE solvers. These trade-offs and related implementation details, which render this new PWTD-enhanced MOT-SIE solver highly scalable on up-to thousands of cores, will be presented at the meeting. The solver has been used to analyze transient electromagnetic scattering from canonical and real-world targets involving up to 10 million spatial unknowns, realizing vast efficiency improvements over its predecessors.