1,721,091 research outputs found
Singular high-order complete vector functions for the analysis and design of electromagnetic structures with Finite Methods
No full textThis dissertation presents new singular curl- and divergence- conforming vector bases that incorporate the edge conditions.
Singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements. The higher order basis functions are obtained as the product of lowest order functions and Silvester–Lagrange interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties are discussed and these bases are proved to be fully compatible with the standard, high-order regular vector bases used in adjacent elements. The curl (divergence) conforming singular bases guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modeling of the curl (divergence), and removal of spurious modes (solutions). These singular high-order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems. Sample numerical results confirm the faster convergence of these bases on wedge problems
Singular high-order complete vector functions for the analysis and design of electromagnetic structures with Finite Methods, PhD dissertation
No full textstampato in Italia, ai sensi dell'art. 1 del decreto legislativo luogotenenziale 31.8.1945, n. 66
Implementation of Higher-Order Two-Dimensional Singular Elements in FEM codes and Numerical Results problems
Full text linkThis paper presents strategies and schemes to implement higher-order two dimensional singular elements in Finite Elements codes. Accurate numerical results are presented and the efficiency of the schemes is discusse
Design of quadrature rules for Müntz and Müntz-logarithmic polynomials using monomial transformation
Full text linkA 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 the number of Gauss-Legendre (GL) quadrature samples and monomial transformation order. To investigate in depth the properties of classical GL quadrature, we present new optimal asymptotic estimates for the remainder. In boundary element integrals this quadrature rule can be applied to evaluate singular functions with end-point singularity, singular kernel as well as smooth functions. The method is numerically stable, efficient, easy to be implemented. The rule has been fully tested and several numerical examples are included. The proposed quadrature method is more efficient in run-time evaluation than the existing methods for Müntz polynomial
Skew Incidence on Concave Wedge With Anisotropic Surface Impedance
Full text linkThe 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 numerical-analytical approach. The numerical results show the spectral properties of the fields, GTD/UTD diffraction coefficients, and total field
Completeness and Regularization Techniques for Wiener-Hopf problems with Discontinuous Layers
Full text linkScattering and radiation by buried multiple objects in multilayered media is of great interest in a vast variety of electromagnetic applications. In this work, we present a general methodology to analyze the complex scattering problems with the capability of semi-analytical method in spectral domain, which allows physical interpretation of the problem and asymptotics estimation of field behavior. The method is based on the combination of the Wiener-Hopf technique, completeness and regularization techniques
The Fredholm Factorization Method Directly Applied to Generalized Wiener-Hopf Equations for Wedge Diffraction Problems in Complex Media
Full text linkIn this work we present a new and comprehensive theory for the solution of electromagnetic diffraction problems involving impenetrable wedges in arbitrary linear media. This theory utilizes Bresler-Marcuvitz transverse equations, characteristic Green’s function procedure, and the Wiener-Hopf technique to address complex scattering problems [1]. The effectiveness of this technique has already been demonstrated in the analysis of wedge problems in isotropic media [2], and now we have extended its application to more general cases [3–4]. We derive Generalized Wiener-Hopf equations (GWHEs) from spectral functional equations in angular regions filled with arbitrary linear media with the application of boundary conditions as solution of transverse equations. These equations can be systematically interpreted with network formalism. We recall that GWHEs have plus and minus unknowns that are defined into different complex planes but related together. We believe that this mathematical technique significantly expands the possibilities for spectral analysis of electromagnetic problems involving angular regions filled with complex arbitrary linear media. We observe that the GWHEs in arbitrary linear media usually report physical unknowns defined into multiple complex planes (more than 2) as the physical problem usually contains more than one propagation constant. Traditional spectral methods such as SommerfeldMalyuzhinets (SM) method, the Kontorovich-Lebedev (KL) transform method, and the Wiener-Hopf (WH) method are fundamental and complementary in studying diffraction problems in presence of sharp discontinuities immersed in isotropic region. The primary benefit in utilizing the SM and KL techniques is the application of the spectral complex angular plane derived from the Sommerfeld integral theory, which has also been successfully applied in the Wiener-Hopf framework through the concept of rotating waves in isotropic angular region, see for instance [2] and references therein. However, the definition of this complex plane is possible in problem with one propagation constant. One of the most important result obtained in presence of anisotropic media is the exact solution obtained by Felsen in the case of the scattering by a PEC wedge immersed in uniaxial medium illuminated by plane waves at normal incidence [5], by applying a generalized version of separation of variables. In the present work, we apply for the first times direct Fredholm factorization [6] to GWHEs avoiding introduction of spectral mapping to resort to CWHEs. In particular the method is effective for problems with more than one propagation constat where the spectral mapping cannot be introduced, and other techniques are ineffective. The fundamental tool in direct Fredholm factorization is the application of Cauchy integral representation to GWHEs that allows to represent unknowns in one complex plane starting from multiple complex planes. With this tool we allow all unknows of GWH problem to be represented using integral equations in one complex plane that can be regularized with Fredholm factorization procedure, see for instance [6, 7]. The proposed methodology is validated through examples, beginning with the examination of diffraction by a PEC wedge in anisotropic media.
This work was supported by Next Generation EU within PNRR M4C2, Inv 1.4-Avv n.3138 16/12/2021-CN00000013 National Centre for HPC, Big Data and Quantum Computing(HPC)
Computation of Potentials on Curvilinear Elements
Full text linkThis paper presents new techniques to compute with an extremely high accuracy the moment integrals of high order vector basis functions on curved patches
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