Overview of Computational Electromagnetics: from Very Low Frequency to Ultra Large Scale Problems

Advances in the microchip industry and nanotechnology call for electromagnetic simulation of structures that are very complex, but are still a tiny fraction of a wavelength. The demand for electromagnetic simulation of antennas on cars, aircraft, and radar scattering, calls for electromagnetic simulation of structures that are many wavelengths long. This talk describes recent advances in solving Maxwell’s equations for complex structures which are a tiny fraction of a wavelength to ultra large structures involving hundreds of wavelength using integral equation methods derived from first principle electromagnetics. Modern electromagnetic simulations often require many degrees of freedom to describe the geometry. Hence, we will describe fast and efficient methods to solve large and dense matrix systems that follow from integral equations.
A comparison between various kinds of numerical methods will be discussed. Then a brief overview of the fast algorithm, the multilevel fast multipole algorithm will be given. Extension of such fast algorithm to layered media and to very low frequencies will be presented. In order to capture quasi-static physics (circuit physics) and wave physics, a numerical solver has to work reliably in the very low frequency regime as well as the wave regime and the quasi-optical regime. Ways to overcome numerical instabilities associated with integral equations as well as acceleration techniques will be discussed.
We will show large-scale simulation examples from scattering, subsurface probing, antennas mounted on cars, and complex structures as encountered in computer circuits and chips.

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Last modified: 02/03/07