The finite-element modeling of three-dimensional electromagnetic fields using edge and nodal elements

Abstract

Abstruct-An efficient and accurate finite-element method is presented for computing transient as well as time-harmonic electromagnetic fields in three-dimensional configurations containing arbitrarily inhomogeneous media that may be anisotropic. To obtain accurate results with an optimum computational efficiency, both consistently linear edge and consistently linear nodal elements are used for approximating the spatial distribution of the field. Compared with earlier work, our formulation is generalized by adding a method for explicitly modeling the normal continuity along interfaces that are free of surface charge. In addition to this the conditions for efficiently solving timeharmonic problems using a code designed for solving transient problems are discussed. Finally a general and simple method for implementing arbitrary inhomogeneous absorbing boundary conditions for modeling arbitrary incident fields is introduced.

An optimization-based approach for solving a time-harmonic multiphysical wave problem with higher-order schemes

“…Further, we multiply (16) by ρ f (x), sum up (16) and (17), and make substitutions v = ∂φ ∂t and v = ∂us ∂t to get the total energy…”

“…In [6], a special procedure suggested by Mur in [16] was used leading to faster convergence to the time-harmonic solution of scattering problems for harmonic planar waves by purely reflecting nonconvex obstacles. That is, they focused on acoustic scattering with sound-soft obstacles and electromagnetic applications with perfectly conducting obstacles.…”

“…The optimization algorithm is considered in Section 6. To guarantee the smooth initial approximation for the CG algorithm we use a transition procedure, suggested by Mur [16]. The main principles of the CG method are presented in Section 6.1.…”

Time-harmonic elasticity with controllability and higher-order discretization methods

“…T for the algorithm are computed with a transition procedure, which is presented in [32]. Values of the control variables e at the ith iteration are denoted by e i 0 and e i 1 .…”

Model-Reduction Method for Electromagnetic Problems

“…Recent research in computational electromagnetics has been widely focused on the development of general-purpose solution methods for electromagnetic problems such as scattering, dielectric cavity resonators, dielectric waveguides, integrated optical waveguides, EMI and EMC studies, VLSI chips and packages, and computer-aided design [1][2][3][4]. According to Maxwell's equations, all of the propagating modes within an inhomogeneous structure are hybrid.…”