Fast Time Domain Integral Equation Solvers for Large-Scale Electromagnetic Analysis

摘要

New fast time domain integral equation (TDIE) solvers for analyzing large-scale electromagnetic scattering and radiation phenomena were developed. These solvers were accelerated using a host of new Plane Wave Time Domain (PWTD) algorithms. PWTD augmented TDIE solvers accomplish for the time domain wave equation (and related Maxwell's equations) what fast multipole methods previously achieved for the Poisson and Helmholtz equations, viz. a significant reduction in computational cost of the integral equation based analysis of large-scale problems through a diagonal representation of field translation operators. The computational cost of analyzing transient surface scattering phenomena using PWTD-enhanced, NOT-based TDIE solvers scales nearly linearly in both the number of spatial and temporal degrees of freedom, that is, far more favorable than that of classical TDIE solvers. The new computational technologies developed were applied to the analysis of scattering and radiation from conducting, resistive, and impedance boundary condition surfaces, penetrable lossless, lossy, and dispersive volumes, potentially residing in layered media, and the analysis of hybrid lumped- distributed microwave circuits involving up to one million spatial unknowns, all this for thousands of time steps. In addition, the technology was successfully applied to the analysis of complex electromagnetic compatibility phenomena of interest to the Air Force and the analysis of surface plasmon polariton propagation problems.