Related papers: Efficient Field-Only Surface Integral Equations fo…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
We study differential equations, describing interaction of electromagnetic field with moving sidebars and surfaces, coming from integral electrodynamics laws. It is shown that differential equations contain but the such features of…
Starting with Maxwell's equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector…
The Electric Field Integral Equation (EFIE) is notorious for its ill-conditioning both in frequency and h-refinement. Several techniques exist for fixing the equation conditioning problems based on hierarchical strategies, Calderon…
We propose a novel method for the efficient and accurate iterative solution of frequency domain integral equations (IEs) that are used for large/multi-scale electromagnetic scattering problems. The proposed method uses a novel…
We derive new general expressions for the fluctuating electromagnetic field outside a homogeneous material surface. The analysis is based on general results from the thermodynamics of irreversible processes, and requires no consideration of…
Considering two-body integral equations we show how they can be dimensionally reduced by integrating exactly over the azimuthal angle of the intermediate momentum. Numerical solution of the resulting equation is feasible without employing a…
The simplest electromagnetic fields' (general- as well as special-relativistic) classification is formulated which is based on physically motivated ideas. According to this classification these fields can belong to three types (electric,…
Conventional electric field integral equation based theory is susceptible to the spurious internal resonance problem when the characteristic modes of closed perfectly conducting objects are computed iteratively. In this paper, we present a…
The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method builds upon the formulation introduced in Bertalmio et al., J. Comput. Phys., 174 (2001),…
The electroencephalography (EEG) forward problem, the computation of the electric potential generated by a known electric current source configuration in the brain, is a key step of EEG source analysis. In this problem, it is often desired…
We consider wave propagation problems in which there is a preferred direction of propagation. To account for propagation in preferred directions, the wave equation is decomposed into a set of coupled equations for waves that propagate in…
The reduction of the three-dimensional classical electromagnetism is performed in a twofold way. In the first case the ordinary two-dimensional electromagnetism is obtained with sources in the form of conserved electric currents flowing…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
We propose and investigate an "interface-flattening" transformation, hinging upon Transformation Optics (T.O.) techniques, to facilitate the rigorous analysis of electromagnetic (EM) fields radiated by sources embedded in tilted,…
The state of art of electromagnetic integral equations has seen significant growth over the past few decades, overcoming some of the fundamental bottlenecks: computational complexity, low frequency and dense discretization breakdown,…
Electric vector potential $\Theta(\boldsymbol{r})$ is a legitimate but rarely used tool to calculate the steady electric field in free-charge regions. Commonly, it is preferred to employ the scalar electric potential $\Phi(\boldsymbol{r})$…
We present a new efficient numerical approach for representing anisotropic physical quantities and/or matrix elements defined on the Fermi surface of metallic materials. The method introduces a set of numerically calculated generalized…
Based on Gauss's law for the electric field, new integral formulas are deduced. Although the applications are not limited within the physics realm, an application is also presented, for the sake of practicability, specifically in the area…
We show that a rectangular collocation method, equivalent to evaluating all matrix elements with a quadrature-like scheme and using more points than basis functions, is an effective approach for solving the electronic Schr\"odinger equation…