Sensitivity analysis for automotive EMC measurements using quasistatic Darwin model

Purpose The purpose of this paper is performing a global sensitivity analysis for automotive electromagnetic compatibility (EMC) measurements related to the CISPR 25 setup in order to examine the effect of the setup uncertainties on the resonance phenomenon. Design/methodology/approach An integral equation formulation is combined with Darwin model and special Green’s functions to model the configuration. The method of Sobol’ indices is used to gain sensitivity factors enhanced with a polynomial chaos metamodel. Findings The proposed model resulted in by orders of magnitude lower number of degrees of freedom and runtime compared to popular numerical methods, e.g. finite element method. The result of the sensitivity study is in good agreement with the underlying physical phenomena and improves the understanding of the resonances. Practical implications The fast model supplemented by the sensitivity factors can be used in EMC design and optimization. Originality/value The proposed method is original in the sense of combining a polynomial chaos metamodel with a low-cost integral equation model to reduce the computational demand for the sensitivity study.

A novel surface-integral-equation formulation for efficient and accurate electromagnetic analyses of near-zero-index structures

We consider accurate and iteratively efficient solutions of electromagnetic problems involving homogenized near-zero-index (NZI) bodies using surface-integral-equation formulations in frequency domain. NZI structures can be practically useful in a plethora of optical applications, as they possess near-zero permittivity and/or permeability values that cannot be found in nature. Hence, numerical simulations are of utmost importance for rigorous design and analyses of NZI structures. Unfortunately, small values of electromagnetic parameters bring computational challenges in numerical solutions of homogeneous models. Conventional formulations available in the literature encounter stability issues that make them inaccurate and/or inefficient as permittivity and/or permeability approach zero. We propose a novel formulation that involves a well-balanced combination of operators and that can provide both accurate and efficient solutions of all NZI cases. Numerical results are presented to demonstrate the superior properties of the developed formulation in comparison to the conventional ones.

Dirac Integral Equations for Dielectric and Plasmonic Scattering

A new integral equation formulation is presented for the Maxwell transmission problem in Lipschitz domains. It builds on the Cauchy integral for the Dirac equation, is free from false eigenwavenumbers for a wider range of permittivities than other known formulations, can be used for magnetic materials, is applicable in both two and three dimensions, and does not suffer from any low-frequency breakdown. Numerical results for the two-dimensional version of the formulation, including examples featuring surface plasmon waves, demonstrate competitiveness relative to state-of-the-art integral formulations that are constrained to two dimensions. However, our Dirac integral equation performs equally well in three dimensions, as demonstrated in a companion paper.

Analysis of the Propagation in High-Speed Interconnects for MIMICs by Means of the Method of Analytical Preconditioning: A New Highly Efficient Evaluation of the Coefficient Matrix

The method of analytical preconditioning combines the discretization and the analytical regularization of a singular integral equation in a single step. In a recent paper by the author, such a method has been applied to a spectral domain integral equation formulation devised to analyze the propagation in polygonal cross-section microstrip lines, which are widely used as high-speed interconnects in monolithic microwave and millimeter waves integrated circuits. By choosing analytically Fourier transformable expansion functions reconstructing the behavior of the fields on the wedges, fast convergence is achieved, and the convolution integrals are expressed in closed form. However, the coefficient matrix elements are one-dimensional improper integrals of oscillating and, in the worst cases, slowly decaying functions. In this paper, a novel technique for the efficient evaluation of such kind of integrals is proposed. By means of a procedure based on Cauchy integral theorem, the general coefficient matrix element is written as a linear combination of fast converging integrals. As shown in the numerical results section, the proposed technique always outperforms the analytical asymptotic acceleration technique, especially when highly accurate solutions are required.

An integral equation formulation of the N-body dielectric spheres problem. Part 2: Complexity analysis

This article is the second in a series of two papers concerning the mathematical study of a boundary integral equation of the second kind that describes the interaction of N dielectric spherical particles undergoing mutual polarisation. The first article presented the numerical analysis of the Galerkin method used to solve this boundary integral equation and derived N-independent convergence rates for the induced surface charges and total electrostatic energy. The current article will focus on computational aspects of the algorithm. We provide a convergence analysis of the iterative method used to solve the underlying linear system and show that the number of liner solver iterations required to obtain a solution is independent of N. Additionally, we present two linear scaling solution strategies for the computation of the approximate induced surface charges. Finally, we consider a series of numerical experiments designed to validate our theoretical results and explore the dependence of the numerical errors and computational cost of solving the underlying linear system on different system parameters.