The scattering of a cylindrical invisibility cloak: reduced parameters and optimization

We investigate the scattering of 2D cylindrical invisibility cloaks with simplified constitutive parameters with the assistance of scattering coefficients. We show that the scattering of the cloaks originates not only from the boundary conditions but also from the spatial variation of the component of permittivity/permeability. According to our formulation, we propose some restrictions to the invisibility cloak in order to minimize its scattering after the simplification has taken place. With our theoretical analysis, it is possible to design a simplified cloak by using some peculiar composites like photonic crystals (PCs) which mimic an effective refractive index landscape rather than offering effective constitutives, meanwhile canceling the scattering from the inner and outer boundaries.Comment: Accepted for J. Phys.

Enhanced A-EFIE with Calderon multiplicative preconditioner

Session: Well-Conditioned Integral Equation Formulations: paper 106.9In this work, a Calderón multiplicative preconditioner (CMP) is proposed for the augmented electric field integral equation (A-EFIE) to improve the convergence. To avoid the imbalance between the vector potential and the scalar potential in the traditional EFIE, A-EFIE considers both the charge and the current as unknowns. After implementing the appropriate frequency scaling and the enforcement of charge neutrality, its formulation is also stable in the low-frequency regime and applicable for large-scale and complex problems. Instead of using other preconditioners, Calderón preconditioning converts the first kind integral equations into the second kind, thus improving the spectrum of the original A-EFIE system. The numerical results show that the resultant system with the combined methods is more stable at low frequencies and converges faster in the calculation of far-field scattering fields.published_or_final_versio

Recent development of surface integral equation solvers for multiscale interconnects and circuits

This paper presents a brief review and recent development of surface integral equation solvers for multiscale interconnects and circuits modeling. As the future production processes down to 5 nm and the operating frequency increases, both multi-scale and large-scale natures should be taken into account in the electromagnetic simulations. Fast, efficient, stable, and broadband integral equation based solvers become indispensable when millions or ten s of millions of unknowns might be involved in the simulation of the integrated circuit. Recent progress and our latest researches in the development of broadband fast electromagnetic solvers will be demonstrated.published_or_final_versio

On characteristic points and approximate decision algorithms for the minimum Hausdorff distance

We investigate {\em approximate decision algorithms} for determining whether the minimum Hausdorff distance between two points sets (or between two sets of nonintersecting line segments) is at most $\varepsilon$.\def\eg{(\varepsilon/\gamma)} An approximate decision algorithm is a standard decision algorithm that answers {\sc yes} or {\sc no} except when $\varepsilon$ is in an {\em indecision interval} where the algorithm is allowed to answer {\sc don't know}. We present algorithms with indecision interval $[\delta-\gamma,\delta+\gamma]$ where $\delta$ is the minimum Hausdorff distance and $\gamma$ can be chosen by the user. In other words, we can make our algorithm as accurate as desired by choosing an appropriate $\gamma$. For two sets of points (or two sets of nonintersecting lines) with respective cardinalities $m$ and $n$ our approximate decision algorithms run in time O(\eg^2(m+n)\log(mn)) for Hausdorff distance under translation, and in time O(\eg^2mn\log(mn)) for Hausdorff distance under Euclidean motion

Calderon preconditioner for the electric field integral equation with layered medium Green's function

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Finite-width gap excitation and impedance models

In this paper, we present a new method for the feed model for the method of moments (MoM). It is derived from a more accurate model with the realistic size of the excitation, in order to replace the commonly-used delta-gap excitation model. This new model is formulated around the electric field integration equations (EFIE) where the terms for magnetic current and magnetic field can be removed. Hence it is much simpler to implement and reduces the numerical complexity. In addition, a variational formulation is derived to provide second order accuracy of the input admittance calculation. Moreover, this new formulation can be easily extended such that one can insert passive load elements of finite size onto the distributive network, without complicated modification of the MoM analysis. This allows simulation of many realistic networks which include load elements such as resistors, capacitors and inductors. © 2011 IEEE.published_or_final_versionThe 2011 IEEE International Symposium on Antennas and Propagation (APSURSI), Spokane, WA., 3-8 July 2011. In IEEE APSURSI Digest, 2011, p. 1297-130

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains

Finite element based generalized impedance boundary condition for complicated em calculation

In this paper, a finite element based generalized impedance boundary condition (FEM-GIBC) is proposed to solve complicated electromagnetic (EM) problems. Complex structures with arbitrary inhomogeneity and shapes are modeled with the finite element method, and their scattering contributions are transformed to generalized impedance conditions on their boundaries. For each sub-domain, a special GIBC can be established and it is only related to the structures in this domain. Hence, for finite periodic structures, a representative GIBC can be formulated at the boundary of a unit cell. After the GIBC at each boundary is established, the electromagnetic coupling between each impedance boundary can be calculated by the boundary integral equations (BIE) and accelerated with the multilevel fast multipole algorithm (MLFMA). © 2011 IEEE.published_or_final_versionThe 2011 IEEE International Symposium on Antennas and Propagation (APSURSI), Spokane, WA., 3-8 July 2011. In IEEE APSURSI Digest, 2011, p. 2700-270

Calderón Preconditioned PMCHWT Equations for Analyzing Penetrable Objects in Layered Medium

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Matching Points with Things

Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point-object pairs. We show that when the objects we match the points to are finite point sets, the problem is NP-complete in general, and polynomial when the objects are on a line or when their number is at most 2. When the objects are line segments, we show that the problem is NP-complete in general, and polynomial when the segments form a convex polygon or are all on a line. Finally, for objects that are straight lines, we show that the problem of finding a min-max non-crossing matching is NP-complete