The computational simulation of time-domain electromagnetic fields within and around complex multi-material structures, such as computers, vehicles, and other engineered structures, has remained a significant challenge. Finite-element and finite-difference approximations for such problems require use of fine volumetric discretizations to counter numerical dispersion and diffusion and, additionally, they generally include extremely small finite elements or mesh sizes to adequately model complex engineered structures. In turn, these fine spatial discretizations require use of extremely small time-steps to ensure stability in the time evolution. As a result, time-domain electromagnetic simulations of complex structures by means of volumetric discretizations require vast amounts of computing time and memory and have thus remained impractical. The proposed approach eliminates all of these challenges. We believe that, on the basis of its highly efficient accelerated frequency-domain solvers, together with the proposed new methodologies for transition from frequency-domain to time-domain solutions, the proposed approach will reset the state of the art in the field of electromagnetic time-domain simulation. Indeed, the proposed solvers can be applied directly to CAD files of the structures under consideration, and they therefore 1)~Account for all geometric details as provided by CAD engineering files; 2)~Do not require use of complex volumetric discretizations; and 3)~Provide highly accurate time-domain solutions by resorting to novel Fourier transform methods from frequency to time, without the multiple challenges arising from time-stepping processes. The previously demonstrated frequency-domain-to-time-domain approach efficiently produces the desired time-domain solutions, and even allows for repeated re-use of the aforementioned frequency-domain solutions for multiple time-domain signals, and design of waveforms optimized to a specific task. In all, the proposed methodology will enable solution of time-domain problems and waveform optimization for highly complex structures and enclosures as illustrated in the proposal text.
