Multiscale computational electromagnetics and applications

Electromagnetic sensing and system-level design problems are often multiscale and very challenging to solve. They remain a significant barrier to system-level sensing and design optimization for a foreseeable future. Such multiscale problems often contain three electrical scales, i.e., the fine scale (geometrical feature size much smaller than a wavelength), the coarse scale (geometrical feature size greater than a wavelength), and the intermediate scale between the two extremes. Most existing commercial solvers are based on single methodologies (such as finite element method or finite-difference time-domain method), and are unable to solve large multiscale problems. We will present our recent work in solving realistic multiscale system-level EM design simulation problems in time domain. The discontinuous Galerkin method is used as the fundamental framework for interfacing multiple scales with finite-element method, spectral element method, and finite difference method. Numerical results show significant advantages of the multiscale method.