A new analysis of scattering problems for electromagnetic crystals consisting of inhomogeneous dielectric materials and conductors

2009 ◽  
Author(s):  
Hongting Jia
Keyword(s):  
Dielectric Materials ◽  
Scattering Problems ◽  
Electromagnetic Crystals ◽  
Inhomogeneous Dielectric

scholarly journals Inhomogeneous dielectrics: conformal mapping and finite-element models

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 839-844 ◽  
Author(s):  
Eugenio Costamagna ◽  
Paolo Di Barba
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Domain Boundary ◽  
Dielectric Materials ◽  
Finite Element Models ◽  
Second Stage ◽  
Inhomogeneous Dielectric ◽  
Long Time ◽  
Relevant Field

AbstractField singularities in electrostatic and magnetostatic fields require special attention in field calculations, and today finite element methods are normally used, both in homogeneous and in inhomogeneous dielectric cases. Conformal mappings are a traditional tool in the homogeneous case, but two-stage Schwarz-Christoffel + Finite Difference procedures have been proposed for a long time to solve problems in case of inhomogeneous dielectric materials too. This allowed to overcome accuracy problems caused by convex corners in the domain boundary and relevant field singularities, and to easily apply finite difference (FD) solvers in rectangular domains. In this paper, compound procedures Schwarz-Christoffel + Finite Elements Method procedures are suggested, to improve both the accuracy and the speed of second stage calculations. The results are compared to Schwarz-Christoffel + Finite Difference and to direct finite-element calculations, and the small differences analyzed considering a well know case study geometry,i.e., a shielded dielectric-supported stripline geometry.

Green’s tensors and associated potentials for electromagnetic waves in inhomogeneous material media

1989 ◽  
Vol 426 (1870) ◽  
pp. 79-106 ◽  
Keyword(s):  
Electromagnetic Waves ◽  
Mathematical Formulation ◽  
Electric Quadrupole ◽  
Source Zone ◽  
Scattering Problems ◽  
Inhomogeneous Dielectric ◽  
Green's Tensor ◽  
Green’S Tensor ◽  
Constitutive Parameters ◽  
Finite Domains

The explicit form of the Green’s tensor in unbounded inhomogeneous dielectric, magnetic and partly conducting material is obtained. The tensor is given explicitly in terms of two scalar Green’s function potentials, each of which obeys its own wave equation. It is found that the gradients of the constitutive parameters at the source of the radiating currents may have a strong effect on the multipolar field. For example, an electric dipole embedded in a uniaxially inhomogeneous source-zone is found to produce additional fields with the characteristics of electric quadrupole ( l = 2, m = ± 1) and a magnetic dipole ( l = 1, m = ± 1). I present a mathematical formulation of Huygens’ principle for inhomogeneous media in terms of the Green’s tensor and its associated tensor potentials, thus extending the use of the Green’s tensor to scattering problems in inhomogeneous finite domains.

scholarly journals Versatile Solver of Nonconformal Volume Integral Equation Based on SWG Basis Function

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Chunbei Luo ◽  
Mingjie Pang ◽  
Hai Lin
Keyword(s):  
Integral Equation ◽  
Basis Function ◽  
High Efficiency ◽  
Low Frequency ◽  
Piecewise Constant Function ◽  
Volume Integral ◽  
Scattering Problems ◽  
Volume Integral Equation ◽  
Inhomogeneous Dielectric ◽  
Brute Force Method

In this paper, a versatile solver of a nonconformal volume integral equation based on the Schaubert-Wilton-Glisson (SWG) basis function is presented. Instead of using a piecewise constant function, the robust conventional SWG basis function is chosen and used directly for discontinuous boundaries. A new map method technique is proposed for constructing SWG pairs, which reduces the complexity from ON2 to ONlogN compared with a brute-force method. The integral equation is solved by the method of moments (MoM) and further accelerated by the multilevel fast multipole algorithm (MLFMA). What’s more, the hybrid scheme of MLFMA and adaptive cross approximation (ACA) is developed to resolve the low-frequency (LF) breakdown when dealing with over-dense mesh objects. Numerical results show that when in analysis of radiation or scattering problems from inhomogeneous dielectric objects or in LF conditions, the proposed solver shows high efficiency without loss of accuracy, which demonstrates the versatile performance of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document