[PDF] Electromagnetic Wave Diffraction By Conducting Screens Pseudodifferential Operators In Diffraction Problems eBook

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Electromagnetic Wave Diffraction by Conducting Screens pseudodifferential operators in diffraction problems

Yu. G. Smirnov
Electromagnetic Wave Diffraction by Conducting Screens pseudodifferential operators in diffraction problems by Yu. G. Smirnov PDF

Author : Yu. G. Smirnov
Publisher : CRC Press
Page : 127 pages
File Size : 43,75 MB
Release : 2022-03-23
Category : Science
ISBN : 0429610564

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This book covers the latest problems of modern mathematical methods for three-dimensional problems of diffraction by arbitrary conducting screens. This comprehensive study provides an introduction to methods of constructing generalized solutions, elements of potential theory, and other underlying mathematical tools. The problem settings, which turn out to be extremely effective, differ significantly from the known approaches and are based on the original concept of vector spaces 'produced' by Maxwell equations. The formalism of pseudodifferential operators enables to prove uniqueness theorems and the Fredholm property for all problems studied. Readers will gain essential insight into the state-of-the-art technique of investigating three-dimensional problems for closed and unclosed screens based on systems of pseudodifferential equations. A detailed treatment of the properties of their kernels, in particular degenerated, is included. Special attention is given to the study of smoothness of generalized solutions and properties of traces.

Electromagnetic Wave Diffraction by Conducting Screens

A. S. Ilʹinskiĭ
Electromagnetic Wave Diffraction by Conducting Screens by A. S. Ilʹinskiĭ PDF

Author : A. S. Ilʹinskiĭ
Publisher :
Page : 114 pages
File Size : 50,66 MB
Release : 2022
Category : Electromagnetic waves
ISBN : 9780138758691

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This book covers the latest problems of modern mathematical methods for three-dimensional problems of diffraction by arbitrary conducting screens. This comprehensive study provides an introduction to methods of constructing generalized solutions, elements of potential theory, and other underlying mathematical tools. The problem settings, which turn out to be extremely effective, differ significantly from the known approaches and are based on the original concept of vector spaces 'produced' by Maxwell equations. The formalism of pseudodifferential operators enables to prove uniqueness theorems and the Fredholm property for all problems studied. Readers will gain essential insight into the state-of-the-art technique of investigating three-dimensional problems for closed and unclosed screens based on systems of pseudodifferential equations. A detailed treatment of the properties of their kernels, in particular degenerated, is included. Special attention is given to the study of smoothness of generalized solutions and properties of traces.

Functional-analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations

Helmut Florian
Functional-analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations by Helmut Florian PDF

Author : Helmut Florian
Publisher : World Scientific
Page : 473 pages
File Size : 12,14 MB
Release : 2001
Category : Mathematics
ISBN : 9812794557

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Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today''s rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations. This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell''s equations, crystal optics, dynamical problems for cusped bars, and conservation laws. Sample Chapter(s). Hyperbolic Equations, Waves and the Singularity Theory (858 KB). Contents: Boundary Value Problems and Initial Value Problems for Partial Differential Equations; Applications of Functional-Analytic and Complex Methods to Mathematical Physics; Partial Complex Differential Equations in the Plane; Complex Methods in Higher Dimensions. Readership: Researchers, lecturers and graduate students in the fields of analysis & differential equations, applied mathematics and mathematical physics.

Functional-analytic And Complex Methods, Their Interactions, And Applications To Partial Differential Equations - Proceedings Of The International Graz Workshop

Helmut Florian
Functional-analytic And Complex Methods, Their Interactions, And Applications To Partial Differential Equations - Proceedings Of The International Graz Workshop by Helmut Florian PDF

Author : Helmut Florian
Publisher : World Scientific
Page : 473 pages
File Size : 32,58 MB
Release : 2001-11-12
Category : Mathematics
ISBN : 9814490008

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Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today's rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations.This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell's equations, crystal optics, dynamical problems for cusped bars, and conservation laws. remove /a remove

Optical Waveguide Theory

Yury Shestopalov
Optical Waveguide Theory by Yury Shestopalov PDF

Author : Yury Shestopalov
Publisher : Springer Nature
Page : 269 pages
File Size : 47,44 MB
Release : 2022-03-26
Category : Science
ISBN : 9811905843

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This book addresses the most advanced to-date mathematical approach and numerical methods in electromagnetic field theory and wave propagation. It presents the application of developed methods and techniques to the analysis of waves in various guiding structures —shielded and open metal-dielectric waveguides of arbitrary cross-section, planar and circular waveguides filled with inhomogeneous dielectrics, metamaterials, chiral media, anisotropic media and layered media with absorption. It also looks into spectral properties of wave propagation for the waveguide families being considered, and the relevant mathematical techniques such as spectral theory of non-self-adjoint operator-valued functions are described, including rigorous proofs of the existence of various types of waves. Further, numerical methods constructed on the basis of the presented mathematical approach and the results of numerical modeling for various structures are also described in depth. The book is beneficial to a broad spectrum of readers ranging from pure and applied mathematicians in electromagnetic field theory to researchers and engineers who are familiar with mathematics. Further, it is also useful as a supplementary text for upper-level undergraduate students interested in learning more advanced topics of mathematical methods in electromagnetics.

Heterogeneous Media

Sergey Kanaun
Heterogeneous Media by Sergey Kanaun PDF

Author : Sergey Kanaun
Publisher : Elsevier
Page : 496 pages
File Size : 14,91 MB
Release : 2020-09-25
Category : Technology & Engineering
ISBN : 0128198818

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Heterogeneous Media: Local Fields, Effective Properties, and Wave Propagation outlines new computational methods for solving volume integral equation problems in heterogeneous media. The book starts by surveying the various numerical methods of analysis of static and dynamic fields in heterogeneous media, listing their strengths and weaknesses, before moving onto an introduction of static and dynamic green functions for homogeneous media. Volume and surface integral equations for fields in heterogenous media are discussed next, followed by an overview of explicit formulas for numerical calculations of volume and surface potentials. The book then segues into Gaussian functions for discretization of volume integral equations for fields in heterogenous media, static problems for a homogeneous host medium with heterogeneous inclusions, volume integral equations for scattering problems, and concludes with a chapter outlining solutions to homogenization problems and calculations of effective properties of heterogeneous media. The book concludes with multiple appendices that feature the texts of basic programs for solving volume integral equations as written in Mathematica. Outlines cutting-edge computational methods for solving volume integral equation problems in heterogeneous media Provides applied examples of approximation and other methods being employed Demonstrates calculation of composite material properties and the constitutive laws for averaged fields within them Covers static and dynamic 2D and 3D mechanical-mathematical models for heterogeneous media