Guido Lombardi

• PhD
• Full Professor at Polytechnic University of Turin

A general theory for solving electromagnetic diffraction problems with impenetrable/penetrable wedges immersed in/made of an arbitrary linear (bianistropic) medium is presented. This novel and general spectral theory handles complex scattering problems by using transverse equations for layered planar and angular structures, the characteristic Green...

Fast and accurate numerical integration always represented a bottleneck in high-performance computational physics, especially in large and multiscale industrial simulations involving Finite (FEM) and Boundary Ele-ment Methods (BEM). The computational demand escalates significantly in problems modelled by irregularor endpoint singular behaviours whi...

In this paper, we study the scattering problem of a truncated grounded slab illuminated by an arbitrarily incident E_z polarized plane wave. We present a solution using the novel semi-analytical spectral method based on an original extension of the Wiener-Hopf technique that uses the concept of characteristic Green’s function and the Fr...

In this work, we introduce a general method to deduce spectral functional equations in elasticity and thus, the generalized Wiener–Hopf equations (GWHEs), for the wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity. The work extends the methodology used in electromagnetic appl...

This book offers a valuable reference for anyone who is already working on or would like to learn more about the analytical and semianalytical methods for wedge diffraction. The authors aim to illustrate the usefulness and elegance of the Wiener–Hopf technique and, in particular, its generalization to the Fredholm method. The text is written in an...

In this work, we introduce a general method to deduce spectral functional equations and, thus, the generalized Wiener–Hopf equations (GWHEs) for wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity with application to electromagnetics. The functional equations are obtained by s...

This chapter discusses the Wiener–Hopf (WH) formulation for the penetrable wedge problems in the context of electromagnetics using the Fredholm factorization method applied to generalized WH equations (GWHEs). Many improvements on the WH method have been made to study the diffraction in the presence of several wedges and layers. The chapter present...

This chapter focuses on the solution of several impedance wedge problems using exact factorization in Wiener–Hopf (WH) equations. It discusses the cases where the considered geometries are amenable to exact solutions using the Sommerfeld–Malyuzhinets method. To recall the WH equations that occur in impenetrable wedge problems, the chapter reconside...

This chapter presents the application of the Fredholm factorization method to generalized Wiener–Hopf equations (GWHEs) for the solution of the general electromagnetic scattering problem, constituted of an impenetrable wedge immersed in a homogeneous medium. The most general problem is the one where the impenetrable wedge is modeled by anisotropic...

This chapter provides a brief history of the classical methods for studying angular regions. While the Sommerfeld–Malyuzhinets method is limited to angular regions where wave equations of Helmholtz type hold, the generalized Wiener‐Hopf technique (GWHT) provides a general method for formulating arbitrary linear wedge problems. The chapter describes...

This chapter focus on a classical canonical problem that is very important in wave motion, i.e. scattering by a half‐plane. It follows, step by step, the solution of Wiener–Hopf (WH) equations using exact closed‐form methodology, and compares it with the more general and effective technique called the Fredholm factorization method. The chapter intr...

In 1931, Wiener and Hopf invented a powerful technique for solving a special type of integral equation. The number of problems that can be effectively approached by the Wiener‐Hopf (WH) technique is significant. This chapter recalls the notations and the fundamental concepts of the WH technique. It introduces a new methodology for the semi‐analytic...

In this article, we present a new methodology in spectral domain to study a novel, complex canonical electromagnetic problem constituted of perfectly electrically conducting (PEC) wedges immersed in complex environments. In particular, we present an arbitrarily flanged dielectric-loaded waveguide that resembles practical structures in scattering an...

The objective of this special issue is to publish papers related to the basic physics of Electromagnetism in thecontext of radio wave propagation, see editorial of Part I [1] .

In his seminal article [1], Gabor observed that Communication theory has up to now been developed mainly on mathematical lines, taking for granted the physical significance of the quantities which figure in its formalism. But communication is the transmission of physical effects from one system to another, hence communication theory should be consi...

Complex scattering targets are often made by structures constituted of wedges that may interact at near field. In this paper we examine the scattering of a plane electromagnetic wave by two separated arbitrarily oriented perfectly electrically conducting (PEC) wedges with parallel axes. The procedure to obtain the solution is based on the recently...

In this paper we examine the scattering of a plane electromagnetic wave by two opposite staggered perfectly electrically conducting (PEC) half-planes immersed in free space by using the Wiener–Hopf technique in the spectral domain. The procedure to obtain the solution is based on the reduction of the factorization problem of matrix Wiener–Hopf equa...

Complex scattering problems are often made by composite structures where wedges and penetrable substrates may interact at near field. In this paper (Part I) together with its companion paper (Part II) we study the canonical problem constituted of a Perfectly Electrically Conducting (PEC) wedge lying on a grounded dielectric slab with a comprehensiv...

Together with Part I, Part II describes the theory, the validation and the application of the Generalized Wiener Hopf Technique (GWHT) to complex scattering problems constituted of wedges and layers that may interact at near field. In particular we present the full analysis of the canonical problem where a Perfectly Electrically Conducting (PEC) we...

Network modeling in electromagnetics is an effective technique in treating scattering problems by canonical and complex structures. Geometries constituted of angular regions (wedges) together with planar layers can now be approached with the Generalized Wiener-Hopf Technique supported by network representation in spectral domain. Even if the networ...

The multilevel nonuniform-grid (MLNG) algorithm, which belongs to the class of "fast" algorithms, is adapted for solving three-dimensional electromagnetic scattering problems. This makes it possible to extend the range of rigorous simulation to significantly higher frequencies and scatterer's sizes than those available for “conventional” methods.

Complex scattering targets are often made by structures constituted by wedges and penetrable substrates which may interact at near field. In this paper, we describe a complete procedure to study this problem with possible developments in radar technologies (like GPR), antenna development, or electromagnetic compatibility (tips near substrates). The...

This paper deals with the problem of evaluating the electromagnetic field of a perfect electrical conducting (PEC) wedge over dielectric substrate. In this paper the directions of the two faces of the wedge are arbitrary. We formulate the problem in terms of generalized Wiener-Hopf equations (GWHE) and we propose a possible method of solution based...

This paper summarizes and disseminates our efforts in developing new techniques to handle singularities in the Method of Moment. In this context singularities are due to mathematical formulation of the problem in terms of integral equations and to the physical properties of the electromagnetic quantities at geometrical/material discontinuities. One...

This paper deals with the problem of evaluating the electromagnetic field of a perfect electrical conductor (PEC) wedge over stratified media. The particular case wherein one face of the wedge is perpendicular to the direction of stratification has been previously considered and solved by using the generalized Wiener-Hopf technique [1]. In this pap...

Scattering targets are often made by complex structures constituted by thin metallic plates as wings, fins, winglets. When thin plates are connected together, they define surface junctions with the possible presence of sharp edges. In this paper we describe a complete procedure to handle junctions in presence of sharp edges in surface integral equa...

This paper presents a novel simple to implement technique to accelerate the method of moments applied to surface integral equations of computational electromagnetics. The method is based on the non-uniform grid algorithm and its precision is enhanced by efficient quadrature rules for the accurate computation of near-field based on the cancellation...

A novel simple to implement technique to accelerate the method of moments applied to surface integral equations of computational electromagnetics is presented. The method is based on the non-uniform grid algorithm and its precision is enhanced by efficient quadrature rules for the accurate computation of near-field based on the cancellation techniq...

A circular cylindrical resonator with metallic (PEC) walls is half-filled with double-negative (DNG) metamaterial that is anti-isorefractive to the double-positive (DPS) material filling the remaining volume of the resonator. The resonance condition of the structure is studied, and it is shown that the resonator may perform independently of diamete...

A perfect electric conductor wedge lying on a dielectric half-space is analyzed, in the frequency domain. The structure is excited by a plane wave coming from the free space region. The problem is formulated using generalized Wiener-Hopf equations and an approximated solution in terms of spectral quantities is proposed by discretization of Fredholm...

Complex scattering targets contain metallic structures with junctions and sharp edges that require a special procedure to be analyzed by the Method of Moments. Singular basis functions to mdel junctions with edge profile connected together are considered. At the Conference, we will show how to handle the different geometrical cases together with nu...

A circular cylindrical metallic resonator with four alternating sectors of DPS and DNG materials is analyzed, in the frequency domain. The two materials are linear, lossless, homogeneous, and anti-isorefractive to each other. The electric field is assumed to be parallel to the cylinder axis. It is also shown that the resonator's dispersion relation...

When the surface integral equation method is applied to study metallic structures with junctions and sharp edges a special procedure to handle the basis functions and the unknowns is required. The paper presents a method to handle junctions of patches with sharp edges. At the Conference, numerical results for current density distributions and scatt...

The diffraction of a plane wave at skew incidence by an arbitrary-angled concave wedge with anisotropic impedance faces is studied. Concave wedges are of interest in wireless propagation models, in particular on modeling buildings and reflectors. The solution is obtained via the generalized Wiener-Hopf technique for arbitrary impedance wedges using...

A circular cylindrical resonator with metallic walls is analyzed in the phasor domain. The resonator contains a wedge of double-negative (DNG) metamaterial that is anti-isorefractive to the double-positive (DPS) material filling the remaining volume of the resonator, and whose edge is located on the resonator axis. The resonance conditions are esta...

A metallic cylindrical resonator partially filled with double-negative (DNG) metamaterial with sector shape is analyzed in the frequency domain. The remaining part of the resonator is filled by a double-positive (DPS) medium. The structure results in a cylindrical resonator of finite length with a metamaterial wedge whose edge is on the cylinder ax...

This paper presents our recent results on the study of the scattering and diffraction of an incident plane wave by wedge structures. A review about the impenetrable wedge problem at skew incidence and about the penetrable wedge at normal incidence is discussed. In particular we focus the attention on the spectral properties of the solution in the a...

The diffraction of an incident plane wave by an isotropic penetrable wedge is studied using generalized Wiener-Hopf equations, and the solution is obtained using analytical and numerical-analytical approaches that reduce the Wiener-Hopf factorization to Fredholm integral equations of second kind. Mathematical aspects are described in a unified and...

This paper presents our recent results on the study of the scattering and diffraction of an incident plane wave by an isotropic penetrable wedge. We have formulated the problem in terms of generalized Wiener-Hopf equations and the solution is obtained using analytical and numerical-analytical approaches that reduce the Wiener-Hopf factorization to...

This paper presents the spectral formulation of the quarter-plane problem using the Wiener-Hopf (W-H) method. The Wiener-Hopf kernels involve analytical functions of two variables. To overcome the difficulties to get the factorization of these kernels we use the Fredholm factorization in two-dimensional spectral domain. The direct numerical solutio...

This paper provides a semi analytical procedure to factorize the two dimensional kernel involved in the quarter plane diffraction problem. The proposed method is based on the reduction of the factorization problem to the solution of a Fredholm integral equation of second kind. The solution of the Fredholm integral equation appears cumbersome since...

This paper considers several target structures containing edges which are useful to validate computer codes developed to the purpose of detecting hidden mines and Unexploded Ordnance (UXO). In particular, we investigate the capabilities of the singular basis functions' approach in Computational Electromagnetics for formulations based on surface int...

The testing integrals used to discretize surface integral equations by application of the Moment Method are usually considered as regular 'trivial' integrals to be computed. This paper discusses some fundamental problems relevant to the numerical evaluation of these integrals and presents several test cases.

A method for constructing the exact quadratures for Müntz and Müntz-logarithmic polynomials is presented. The algorithm does permit to anticipate the precision (machine precision) of the numerical integration of Müntz-logarithmic polynomials in terms of number of Gauss-Legendre quadrature samples and monomial transformation order. To investigate in...

This paper reports the state of the art on the study of diffraction by a dielectric wedge and it proposes a new method to compute the diffracted field. In particular the paper presents the application of the Wiener-Hopf method to the problem of diffraction of a plane wave by a dielectric wedge immersed in free space. The formulation and the equatio...

This paper presents the properties and the rules to define subsectional singular divergence-conforming vector bases that incorporate the edge conditions for wedge structures. The use of singular high-order bases in Method of Moment codes provides highly accurate and efficient numerical results for the current and charge density induced on 3D sharp-...

The aim of our work is to provide an efficient approximate evaluation of the diffraction coefficients of a dielectric wedge starting by the WH formulation. An advantage of this approach is constituted by its capability to formulate and solve the more general wedge problems that involve anisotropic or bianisotropic media. This method seems to extend...

The paper summarizes the research results obtained on numerical modeling of the diffraction effects due to abrupt material or geometrical discontinuities of electromagnetic structures. High order polynomial vector bases are often used to numerically model EM problems, but polynomial approximations spoil the convergence properties of the used finite...

We present new subsectional, singular divergence-conforming vector bases that incorporate the edge conditions for conducting wedges. The bases are of additive kind because obtained by incrementing the regular polynomial vector bases with other subsectional basis sets that model the singular behavior of the unknown vector field in the wedge neighbor...

A new technique for machine precision evaluation of singular and nearly singular potential integrals with 1/R singularities is presented. The numerical quadrature scheme is based on a new rational expression for the integrands, obtained by a cancellation procedure. In particular, by using library routines for Gauss quadrature of rational functions...

A general theory to factorize the Wiener-Hopf (W-H) kernel using Fredholm Integral Equations (FIE) of the second kind is presented. This technique, hereafter called Fredholm factorization, factorizes the W-H kernel using simple numerical quadrature. W-H kernels can be either of scalar form or of matrix form with arbitrary dimensions. The kernel spe...

The diffraction of an arbitrary incident plane wave on two opposite PEC half-planes is formulated in terms of Wiener-Hopf equations. The factorization of the 4x4 matrix kernel is reduced to the factorization of a 2x2 matrix kernel. The factorization of the kernel is obtained by the solution of a Fredholm equation of second kind that provides very a...

This paper describes a new numerical technique based on the cancellation method to compute singular and nearly singular potential integrals with machine precision.

This paper describes a new numerical technique to compute singular and nearly singular potential integrals with machine precision by working directly in the parent reference-frame.

A new Wiener-Hopf approach for the solution of impenetrable wedges at skew incidence is presented. Mathematical aspects are described in a unified and consistent theory for angular region problems. Solutions are obtained using analytical and numerical-analytical approaches. Several numerical tests from the scientific literature validate the new tec...

Recently the diffraction by arbitrary impenetrable wedges has been reduced to the factorization of matrices of order four. This paper provides an efficient and general factorization technique that is based on the solution of a Fredholm integral equation of second kind

This paper describes the fundamental properties of new singular vector bases that incorporate the edge conditions in curved triangular elements. The bases are fully compatible with the interpolatory or hierarchical high-order regular vector bases used in adjacent elements. Several numerical results confirm the faster convergence of these bases on w...

The authors explore various possible approaches for generating lowest order and higher order bases for modeling surface currents and their divergence for moment method application to integral equations. The bases developed are defined on curved triangular and quadrilateral elements. All the bases are conveniently defined in parent element coordinat...