Anton Menshov

Novel single-source integral equation in electromagnetics

New single-source integral equation (SSIE) of computational electromagnetics has been recently proposed. Unlike the previously known SSIEs which are derived from traditional surface integral equations (IE) through elimination of either electric or magnetic equivalent current, the new SSIE is obtained from the volume IE stated for homogeneous objects. Thus far, the novel electric field SSIE has been demonstrated to be applicable to the problems of magneto-quasi-statics with both homogeneous and layered medium background. It has been also successfully applied to both the scalar and vector problems of full-wave scattering on homogeneous penetrable 2D scatterers. This paper overviews the novel SSIE and problems to which it has been successfully applied to.

Surface–Volume–Surface Electric Field Integral Equation for Magneto-Quasi-Static Analysis of Complex 3-D Interconnects

A novel single-source surface-volume-surface integral equation is proposed for accurate broadband resistance and inductance extraction in 3-D interconnects. The new equation originates in the volume integral equation (VIE) traditionally used for magneto-quasi-static modeling of current flow in 3-D wires. The latter is reduced to a surface integral equation by representing the electric field inside each conductor segment as a superposition of cylindrical waves emanating from the conductors boundary. As no approximation is utilized and all underlying boundary conditions and pertinent equations are satisfied in the reduction, the new integral equation is rigorously equivalent to the solution of the traditional volume electric field integral equation. The rigorous nature of the proposed single-source surface integral equation is corroborated numerically. In this paper, a detailed description of the method of moments discretization for the proposed surface integral equation is also presented. Numerical solution of the proposed surface integral equation for a 12-conductor bond-wire package is used to demonstrate the accuracy of the method and its computational benefits compared to the traditional solution based on the VIE.

A fast direct integral-equation solver for hydraulic fracture diagnosis

An ℋ-matrix based fast direct solver is presented to accelerate the solution of volume integral equations pertinent to the analysis of hydraulic fracture resistivity measurements. The solvers performance for this problem type is compared to that of an FFT-accelerated iterative solver.

Accurate transmission lines characterization via higher order moment method solution of novel single-source integral equation

A new method for high precision extraction of per-unit-length inductance and resistance in the multi-conductor transmission lines (MTLs) is presented. The approach is based on higher-order geometrical representation of the MTL cross-section followed by higher-order method of moment discretization of a novel surface single-source integral equation. Through comparison against the analytically available solutions, the method is shown to achieve 6 digits of precision in the extracted MTLs resistance (R) and inductance (L) using moderate computational resources. The proposed approach paves a way for numerically inexpensive characterization of MTLs of arbitrary cross-sections with analytic-like quality.

Novel single-source integral equation for inductance extraction in transmission lines embedded in lossy layered substrates

A novel surface integral equation (IE) formulation for magneto-quasi-static analysis of current flow in two-dimensional conductors situated in lossy layered substrates is proposed. Traditional approach is based on the volume IE formulated with respect to the unknown current distribution in the conductors cross-section. In this work, we transform the volume IE to a surface IE via representation of the volumetric current density as a superposition of the waves emanating from the conductors boundaries. The resulting surface IE features a single unknown surface current density unlike the traditional surface IEs which require both electric and magnetic surface current densities. Also, the resultant single-source surface IE formulation involves only the electric field Greens functions instead of both electric and magnetic field Greens functions as required by the traditional surface IE formulations. The latter property makes the proposed IE formulation particularly suitable for analysis of current flow in conductors embedded in lossy layered substrates.

Toward predictive modeling of full-size packages with layered-medium integral-equation methods

Layered-medium integral-equation (LMIE) methods that can confront the multiscale problems encountered in electromagnetic modeling of electronic packages are presented. The methods include (i) an impedance-boundary condition (IBC) formulation for modeling conductor thickness, roughness, and finite conductivity, (ii) non-radiating lumped-port models for extracting network parameters, and (iii) FFT based iterative and hierarchical-matrix (ℋ-matrix) based direct algorithms for efficiently solving the resulting systems of equations. The methods are used to analyze increasingly higher fidelity models of a benchmark packaging interconnect structure; the results are validated with measurements; and the tradeoff between increased model fidelity and computational costs are quantified.

An ℋ-matrix accelerated direct solver for fast analysis of scattering from structures in layered media

Frequency-domain mixed-potential integral-equations are commonly used for analyzing scattering from structures residing in layered backgrounds (K. A. Michalski and D. Zheng, IEEE TAP, 38(3), 335–344, 1990). Their traditional direct method-of-moments solution based on LU-decomposition is limited to small problems, however, because it requires O(N2) operations to fill the N × N dense impedance matrix (with a large constant in front of the complexity estimate because of the high cost of computing Sommerfeld integrals), O(N3) operations to factorize the impedance matrix, and O(N rhs N2) operations to find the solution for N rhs different excitations. Moreover, modern fast iterative algorithms that enabled the solution of extreme problems for homogeneous backgrounds are often inapplicable, inefficient, or must be modified significantly (K. Yang and A. E. Yilmaz, CEM Int. Workshop, 2013) for layered backgrounds because of the more complicated Green functions. In this article, a fast direct solver based on the hierarchical matrix (ℋ-matrix) framework (W. Hackbusch, Computing, 62, 89–108, 1999) is used to accelerate the analysis of scattering from structures residing in layered media.

A modified admissibility criterion for H-matrix based integral-equation solvers

An alternative matrix block hierarchy construction process is presented for Ή-matrix based fast direct solvers. In the proposed method, the traditional distance-based criterion for admitting a given block of the impedance matrix is augmented by also evaluating the admissibility of its children blocks.

New Vector Single-Source Surface Integral Equation for Scattering Problems on Dielectric Objects in 2-D

A new surface single-source integral equation (SSIE) is proposed for the solution of electromagnetic wave scattering problems in two dimensions. The traditional volume electric field integral equation (V-EFIE) is reduced to the new single-source surface integral equation by representing the electric field inside the scatterer as a superposition of cylindrical waves emanating from its boundary. While being rigorous in nature, the new single-source surface integral equation features half of the degrees of freedom compared with traditional surface integral equation formulations. It is amenable to derivative-free method of moments discretization as it features only electric-field-type of Green’s function instead of both electric and magnetic field Green’s functions.

Microwave imaging with contrast source inversion method in focusing media

The Contrast Source Inversion (CSI) algorithm is numerically implemented and tested for microwave tomography (MWT) of 2-D objects in the presence of the focusing media. The focusing media in the novel implementation of the CSI algorithm is formed by the Veselago Lens. Unlike in the conventional CSI algorithm implemented in non-focusing media, the presence of the lens produces diagonal dominance in the discretized inverse problem operator thus eliminating its rank deficiency. This diagonal dominance of the discretized inverse problem operator matrix is shown to notably speed up converges of the conjugate gradient (CG) optimization inherent to the CSI method and reduces the final error in the object reconstruction which the CG iterations saturate at.