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In this paper we present a new regularized electric flux volume integral equation (D-VIE) for modeling high-contrast conductive dielectric objects in a broad frequency range. This new formulation is particularly suitable for modeling…

Many integral equations used to analyze scattering, such as the standard combined field integral equation (CFIE), are not well-conditioned for a wide range of frequencies and multi-scale geometries. There has been significant effort to…

An Integral Equation (IE) based electromagnetic field solver using metasurface susceptibility tensors is proposed and validated using variety of numerical examples in 2D. The proposed method solves for fields generated by the metasurface…

This paper presents a new method, based on the well-known method of moments (MoM), for the numerical electromagnetic analysis of scattering and radiation from metallic or dielectric structures, or both structure types in the same…

A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…

Strong-Field Electrodynamics (SFE) is Maxwell theory with a certain Lorentz-covariant Ohm's law which uses only the electromagnetic degrees of freedom. We show that SFE is {\it semi-dissipative}: while the dissipation rate of the…

The state of art of time domain integral equation (TDIE) solvers has grown by leaps and bounds over the past decade. During this time, advances have been made in (i) the development of accelerators that can be retrofitted with these solvers…

We propose a novel approach to the linear viscoelastic problem of shear-deformable geometrically exact beams. The generalized Maxwell model for one-dimensional solids is here efficiently extended to the case of arbitrarily curved beams…

This paper analyzes how hierarchical bases preconditioners constructed for the Electric Field Integral Equation (EFIE) can be effectively applied to the Combined Field Integral Equation (CFIE). For the case where no hierarchical solenoidal…

A transient Mie-like solution for acoustic scattering from a spherical object is derived within a mesh-free and singularity-free Time Domain Integral Equation (TDIE) framework for the sound-soft, sound-rigid and penetrable cases. The method…

For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation…

In a recent paper, Klaseboer et al. (IEEE Trans. Antennas Propag., vol. 65, no. 2, pp. 972-977, Feb. 2017) developed a surface integral formulation of electromagnetics that does not require working with integral equations that have singular…

Stability of time domain integral equation (TDIE) solvers has remained an elusive goal for many years. Advancement of this research has largely progressed on four fronts: (1) Exact integration, (2) Lubich quadrature, (3) smooth temporal…

Helmholtz decompositions of the elastic fields open up new avenues for the solution of linear elastic scattering problems via boundary integral equations (BIE) [Dong, Lai, Li, Mathematics of Computation,2021]. The main appeal of this…

Voltage breakdown in high-voltage pulsed vacuum systems arises from nonlinear multiscale interactions among circuit dynamics, kinetic plasma evolution, and ion-induced secondary electron emission (SEE) at electrode surfaces. Although…

A thin-sheet (TS) volume integral equation (VIE) formulation incorporating generalized sheet transition conditions (GSTCs) is presented for the simulation of three-dimensional (3D) bianisotropic metasurfaces. The metasurface is represented…

We present several versions of Regularized Combined Field Integral Equation (CFIER) formulations for the solution of three dimensional frequency domain electromagnetic scattering problems with Perfectly Electric Conducting (PEC) boundary…

The well-known "Sommerfeld radiation problem" of a small -Hertzian- vertical dipole above flat lossy ground is reconsidered. The problem is examined in the spectral domain, through which it is proved to yield relatively simple integral…

An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of…

We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and…