Computational electromagnetics: the physics of smooth versus oscillatory fields

Abstract

This paper starts by discussing the difference in the physics between solutions to Laplace's equation (static) and Maxwell's equations for dynamic problems (Helmholtz equation). Their differing physical characters are illustrated by how the two fields convey information away from their source point. The paper elucidates the fact that their differing physical characters affect the use of Laplacian field and Helmholtz field in imaging. They also affect the design of fast computational algorithms for electromagnetic scattering problems. Specifically, a comparison is made between fast algorithms developed using wavelets, the simple fast multipole method, and the multi-level fast multipole algorithm for electrodynamics. The impact of the physical characters of the dynamic field on the parallelization of the multi-level fast multipole algorithm is also discussed. The relationship of diagonalization of translators to group theory is presented. Finally, future areas of research for computational electromagnetics are described.

A high order hybrid finite element method applied to the solution of electromagnetic wave scattering problems in the time domain

“…Although techniques based upon the use of integral equations are often the best approach for problems that just involve wave scattering [4,8], volume based methods appear to offer many advantages when the full range of applications needs to be considered [14]. For the analysis of electromagnetic wave scattering problems, an established computational volume based method for the solution of Maxwell's equations is the explicit finite difference time domain (FDTD) scheme [39].…”

Multiband printed and double‐sided dipole antenna for WLAN/WiMAX applications

“…In the experimental results, we noted improved efficiency of the proposed amplifier, while its output power was nearly identical to that of a normal amplifier. A power amplifier is an essential building block in wireless communication systems [1][2][3][4][5]. Additionally, the power amplifier is regarded as the component which determines the power efficiency of the overall mobile system, as the amplifier consumes most of the power from the battery.…”

“…When the wavelength is sizeable compared to the structure, wave physics becomes important. It is important for a simulation method to capture proper physics at different frequency bands [2]. When a structure is multiscale, it has parts that are small compared to wavelength, and parts that are on the order of wavelength.…”

Integral equation solvers for real world applications - some challenge problems

“…There is a major difference between static (or low frequency, non-oscillatory) fields and dynamic, oscillatory fields [5] Static fields have the property that they are infinitely smooth away from the source point, in the sense that their higher order derivatives are vanishingly small. On the other hand, dynamic fields have higher order derivatives that do not vanish away from the source point.…”