Fast direct volume integral equation solvers for large-scale general electromagnetic analysis.

摘要

Among existing computational electromagnetic methods, volume integral equation (VIE) based methods have unique advantages in modeling both open-region problems and complicated geometry and materials. However, to accentuate the unique advantages of the VIE-based methods, two major obstacles must be overcome: one is the generality of the VIE formulation; the other being the high computational cost of a VIE-solver.;Traditional VIE-based formulations developed for solving wave-related problems are not amenable for solving circuit problems, while existing circuit-based VIE-formulations involve simplifications and approximations that are invalid for wave-related problems. In this work, we develop a new first-principles-based VIE-formulation that bridges the gap between wave- and circuit-based electromagnetic analysis, using which the analysis and design of circuits exposed to external electromagnetic fields is made possible in a full electromagnetic spectrum.;The linear system of equations resulting from a VIE-based analysis is not only dense but also large involving volume unknowns in a 3-D computational domain. To address this computational challenge, we overcame the related numerical issues to develop an H2-matrix based linear complexity direct VIE solver for large-scale circuit parameter extraction, which is capable of solving millions of VIE unknowns using modest computational resources on a single CPU core. Lastly, our newly developed minuscule cost SVD-mimicking H2-matrix recompression schemes have made it possible, for the first time, to achieve O( N) iterative and O(NlogN) direct VIE solvers for general large-scale electrodynamic scattering problems.