Electromagnetic Analysis for Conductive Media Based on Volume Integral Equations

Abstract

Accurate electromagnetic (EM) analysis for conductive media requires to consider the finite conductivity of the media. Although the problems can be formulated by surface integral equations (SIEs) with an approximate surface impedance, we treat the conductive media as penetrable objects and use volume integral equations (VIEs) to exactly describe their EM features. The VIEs are solved by a point-matching scheme which does not rely on any basis and testing functions and allows the use of nonconforming meshes. Since the VIEs are well-conditioned in general and the integral kernels are free of material parameters, the scheme is flexible to accommodate a wide range of skin depth. Moreover, when the skin depth is small, we can only discretize the skin domain with a current distribution to reduce the cost. For large conductive media, we also incorporate the scheme with the multilevel fast multipole algorithm (MLFMA) to accelerate the solution. Typical numerical examples are presented to illustrate the scheme and its effectiveness has been validated.Index Terms-Conductive media, electromagnetic analysis, multilevel fast multipole algorithm, point-matching method, volume integral equations.

Improved hybrid discretisation of volume integral equation with the characteristic basis function method for analysing scattering from complex dielectric objects

“…The accurate electromagnetic (EM) analysis is essential in many engineering applications [1,2], such as designing electronic devices, wireless communication, EM compatibility, microwave imaging etc. In the real world, these analysed targets usually include complex dielectric structures, which rely on the accurate method of moments (MoM) solution of volume integral equation (VIE) [3][4][5][6][7][8][9][10]. Compared with the surface integral equation (SIE) solvers, the VIE solvers which allow the complexity of geometries and the inhomogeneity of materials are more competitive for analysing the dielectric objects [11,12].…”

Optimization of block size for volume integral equation‐based characteristic basis function method

“…1,2 Since the VIE is a second kind of Fredholm integral equation, the impedance matrix derived from the method of moments (MoM) solution of VIE is well-conditioned in general. 3 Compared with surface integral equation (SIE), 4 the VIE shows higher flexibility and efficiency in modeling dielectric objects consisting of various materials or multiscale structures. 5 Moreover, the integral kernel of VIE which depends on free-space Green's function is free of dielectric properties, providing a remarkable convenience to employ fast numerical algorithms.…”

“…In the past few years, volume integral equation (VIE) has gained popularity in the area of analyzing electromagnetic scattering from inhomogeneous dielectric objects 1,2 . Since the VIE is a second kind of Fredholm integral equation, the impedance matrix derived from the method of moments (MoM) solution of VIE is well‐conditioned in general 3 . Compared with surface integral equation (SIE), 4 the VIE shows higher flexibility and efficiency in modeling dielectric objects consisting of various materials or multiscale structures 5 .…”

On the Ewald Oseen scattering formulation for light scattering: stability, singularity and parallelization

“…Secondly, there is the issue of the singular integrals that appear when the integral part of the EOS algorithm is discretized. This issue is very much present in BEM and in TBEM [12][13][14][15], but they are more prevalent and severe for the EOS formulation, where we have to tackle both surface integrals and volume integrals. We believe that the type of singular integrals, and how to treat them for the case of light scattering, are fairly representative for the level of complexity one will encounter, while applying the EOS approach to wave scattering problems.…”