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Mapped Vector Basis Functions For Electromagnetic Integral Equations
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Book Synopsis Mapped Vector Basis Functions for Electromagnetic Integral Equations by : Andrew F. Peterson
Download or read book Mapped Vector Basis Functions for Electromagnetic Integral Equations written by Andrew F. Peterson and published by Morgan & Claypool Publishers. This book was released on 2006 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method-of-moments solution of the electric field and magnetic field integral equations (EFIE and MFIE) is extended to conducting objects modeled with curved cells. These techniques are important for electromagnetic scattering, antenna, radar signature, and wireless communication applications. Vector basis functions of the divergence-conforming and curl-conforming types are explained, and specific interpolatory and hierarchical basis functions are reviewed. Procedures for mapping these basis functions from a reference domain to a curved cell, while preserving the desired continuity properties on curved cells, are discussed in detail. For illustration, results are presented for examples that employ divergence-conforming basis functions with the EFIE and curl-conforming basis functions with the MFIE. The intended audience includes electromagnetic engineers with some previous familiarity with numerical techniques.
Book Synopsis Mapped Vector Basis Functions for Electromagnetic Integral Equations by : Andrew Peterson
Download or read book Mapped Vector Basis Functions for Electromagnetic Integral Equations written by Andrew Peterson and published by Springer Nature. This book was released on 2022-06-01 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method-of-moments solution of the electric field and magnetic field integral equations (EFIE and MFIE) is extended to conducting objects modeled with curved cells. These techniques are important for electromagnetic scattering, antenna, radar signature, and wireless communication applications. Vector basis functions of the divergence-conforming and curl-conforming types are explained, and specific interpolatory and hierarchical basis functions are reviewed. Procedures for mapping these basis functions from a reference domain to a curved cell, while preserving the desired continuity properties on curved cells, are discussed in detail. For illustration, results are presented for examples that employ divergence-conforming basis functions with the EFIE and curl-conforming basis functions with the MFIE. The intended audience includes electromagnetic engineers with some previous familiarity with numerical techniques.
Book Synopsis Integral Equation Methods for Electromagnetic and Elastic Waves by : Weng Cho Chew
Download or read book Integral Equation Methods for Electromagnetic and Elastic Waves written by Weng Cho Chew and published by Morgan & Claypool Publishers. This book was released on 2009 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods. Table of Contents: Introduction to Computational Electromagnetics / Linear Vector Space, Reciprocity, and Energy Conservation / Introduction to Integral Equations / Integral Equations for Penetrable Objects / Low-Frequency Problems in Integral Equations / Dyadic Green's Function for Layered Media and Integral Equations / Fast Inhomogeneous Plane Wave Algorithm for Layered Media / Electromagnetic Wave versus Elastic Wave / Glossary of Acronyms
Book Synopsis Green's Function Integral Equation Methods in Nano-Optics by : Thomas M. Søndergaard
Download or read book Green's Function Integral Equation Methods in Nano-Optics written by Thomas M. Søndergaard and published by CRC Press. This book was released on 2019-01-30 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive introduction to Green’s function integral equation methods (GFIEMs) for scattering problems in the field of nano-optics. First, a brief review is given of the most important theoretical foundations from electromagnetics, optics, and scattering theory, including theory of waveguides, Fresnel reflection, and scattering, extinction, and absorption cross sections. This is followed by a presentation of different types of GFIEMs of increasing complexity for one-, two-, and three-dimensional scattering problems. In GFIEMs, the electromagnetic field at any position is directly related to the field at either the inside or the surface of a scattering object placed in a reference structure. The properties of the reference structure, and radiating or periodic boundary conditions, are automatically taken care of via the choice of Green’s function. This book discusses in detail how to solve the integral equations using either simple or higher-order finite-element-based methods; how to calculate the relevant Green’s function for different reference structures and choices of boundary conditions; and how to calculate near-fields, optical cross sections, and the power emitted by a local source. Solution strategies for large structures are discussed based on either transfer-matrix-approaches or the conjugate gradient algorithm combined with the Fast Fourier Transform. Special attention is given to reducing the computational problem for three-dimensional structures with cylindrical symmetry by using cylindrical harmonic expansions. Each presented method is accompanied by examples from nano-optics, including: resonant metal nano-particles placed in a homogeneous medium or on a surface or waveguide; a microstructured gradient-index-lens; the Purcell effect for an emitter in a photonic crystal; the excitation of surface plasmon polaritons by second-harmonic generation in a polymer fiber placed on a thin metal film; and anti-reflective, broadband absorbing or resonant surface microstructures. Each presented method is also accompanied by guidelines for software implementation and exercises. Features Comprehensive introduction to Green’s function integral equation methods for scattering problems in the field of nano-optics Detailed explanation of how to discretize and solve integral equations using simple and higher-order finite-element approaches Solution strategies for large structures Guidelines for software implementation and exercises Broad selection of examples of scattering problems in nano-optics
Book Synopsis Analysis and Implementation of Isogeometric Boundary Elements for Electromagnetism by : Felix Wolf
Download or read book Analysis and Implementation of Isogeometric Boundary Elements for Electromagnetism written by Felix Wolf and published by Springer Nature. This book was released on 2020-11-30 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive mathematical and computational approach for solving electromagnetic problems of practical relevance, such as electromagnetic scattering and the cavity problems. After an in-depth introduction to the mathematical foundations of isogeometric analysis, which discusses how to conduct higher-order simulations efficiently and without the introduction of geometrical errors, the book proves quasi-optimal approximation properties for all trace spaces of the de Rham sequence, and demonstrates inf-sup stability of the isogeometric discretisation of the electric field integral equation (EFIE). Theoretical properties and algorithms are described in detail. The algorithmic approach is, in turn, validated through a series of numerical experiments aimed at solving a set of electromagnetic scattering problems. In the last part of the book, the boundary element method is combined with a novel eigenvalue solver, a so-called contour integral method. An algorithm is presented, together with a set of successful numerical experiments, showing that the eigenvalue solver benefits from the high orders of convergence offered by the boundary element approach. Last, the resulting software, called BEMBEL (Boundary Element Method Based Engineering Library), is reviewed: the user interface is presented, while the underlying design considerations are explained in detail. Given its scope, this book bridges an important gap between numerical analysis and engineering design of electromagnetic devices.
Book Synopsis A Combination of Rao-Wilton-Glisson and Asymptotic Phase Basis Functions to Solve the Electric and Magnetic Field Integral Equations by : John Robert Gulick
Download or read book A Combination of Rao-Wilton-Glisson and Asymptotic Phase Basis Functions to Solve the Electric and Magnetic Field Integral Equations written by John Robert Gulick and published by . This book was released on 2001 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using the method of moments to solve the electric and magnetic field integral equations for the currents on a PEC surface requires a large number of unknowns to capture the current's rapid spatial variation across the surface. Rao-Wilton-Glisson (RWG) vector basis functions 1 have been successfully used for the past twenty years 1, 2, 3,.... Unfortunately, the required number of unknowns is on the order of 100 per square wavelength making electrically large problems impractical. For large smooth objects, the rapid spatial variation in the current is due to phase variations rather than magnitude variations. Thus, using asymptotic phase (AP) basis functions can drastically reduce the number of unknowns 3 for large, smooth metallic bodies. The A') basis flinction incorporates the anticipated phase, hence represents a more efficient basis function for a large class of problems. However, using RWG basis functions for monostatic calculations is more efficient since the matrix entries need not be recomputed for each new incidence angle, as is the case for an AP expansion. One can combine the methods; selecting RWG or AP basis functions for a given geometry based on an element's location within the geometry. This allows the relaxation of mesh density in smooth flat regions not near the discontinuities resulting in a significant reduction of unknowns. This research shows that combining functions is highly efficient and the effectiveness of this method depends on the geometry of application.
Book Synopsis Synthesis Series in Computational Electromagnetics Volume 1 by : Andrew Peterson
Download or read book Synthesis Series in Computational Electromagnetics Volume 1 written by Andrew Peterson and published by Morgan & Claypool. This book was released on 2010-10-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume in a series of hardcovers combining Synthesis Lectures. This volume contains the following Synthesis books: Mapped Vector Basis Function for Electromagnetic Integral Equations; MRTD (Multi Resolution Time Domain) Method in Electromagnetics; and Higher Order FDTD Schemes for Waveguide and Antenna Structures.
Book Synopsis Numerical Methods in Photonics by : Andrei V. Lavrinenko
Download or read book Numerical Methods in Photonics written by Andrei V. Lavrinenko and published by CRC Press. This book was released on 2018-09-03 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulation and modeling using numerical methods is one of the key instruments in any scientific work. In the field of photonics, a wide range of numerical methods are used for studying both fundamental optics and applications such as design, development, and optimization of photonic components. Modeling is key for developing improved photonic devices and reducing development time and cost. Choosing the appropriate computational method for a photonics modeling problem requires a clear understanding of the pros and cons of the available numerical methods. Numerical Methods in Photonics presents six of the most frequently used methods: FDTD, FDFD, 1+1D nonlinear propagation, modal method, Green’s function, and FEM. After an introductory chapter outlining the basics of Maxwell’s equations, the book includes self-contained chapters that focus on each of the methods. Each method is accompanied by a review of the mathematical principles in which it is based, along with sample scripts, illustrative examples of characteristic problem solving, and exercises. MATLAB® is used throughout the text. This book provides a solid basis to practice writing your own codes. The theoretical formulation is complemented by sets of exercises, which allow you to grasp the essence of the modeling tools.
Book Synopsis Integral Equations and Iteration Methods in Electromagnetic Scattering by : A. B. Samokhin
Download or read book Integral Equations and Iteration Methods in Electromagnetic Scattering written by A. B. Samokhin and published by Walter de Gruyter. This book was released on 2013-03-12 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics by : Stephen Gedney
Download or read book Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics written by Stephen Gedney and published by Springer Nature. This book was released on 2022-05-31 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to practical problems in engineering and science. Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics guides the reader through the foundational theory of the FDTD method starting with the one-dimensional transmission-line problem and then progressing to the solution of Maxwell's equations in three dimensions. It also provides step by step guides to modeling physical sources, lumped-circuit components, absorbing boundary conditions, perfectly matched layer absorbers, and sub-cell structures. Post processing methods such as network parameter extraction and far-field transformations are also detailed. Efficient implementations of the FDTD method in a high level language are also provided. Table of Contents: Introduction / 1D FDTD Modeling of the Transmission Line Equations / Yee Algorithm for Maxwell's Equations / Source Excitations / Absorbing Boundary Conditions / The Perfectly Matched Layer (PML) Absorbing Medium / Subcell Modeling / Post Processing
Book Synopsis Analysis and Design of Substrate Integrated Waveguide Using Efficient 2D Hybrid Method by : Xuan Hui Wu
Download or read book Analysis and Design of Substrate Integrated Waveguide Using Efficient 2D Hybrid Method written by Xuan Hui Wu and published by Springer Nature. This book was released on 2022-06-01 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Substrate integrated waveguide (SIW) is a new type of transmission line. It implements a waveguide on a piece of printed circuit board by emulating the side walls of the waveguide using two rows of metal posts. It inherits the merits both from the microstrip for compact size and easy integration, and from the waveguide for low radiation loss, and thus opens another door to design efficient microwave circuits and antennas at a low cost. This book presents a two-dimensional fullwave analysis method to investigate an SIW circuit composed of metal and dielectric posts. It combines the cylindrical eigenfunction expansion and the method of moments to avoid geometrical descritization of the posts. The method is presented step-by-step, with all the necessary formulations provided for a practitioner who wants to implement this method by himself. This book covers the SIW circuit printed on either homogeneous or inhomogeneous substrate, the microstrip-to-SIW transition and the speed-up technique for the simulation of symmetrical SIW circuits. Different types of SIW circuits are shown and simulated using the proposed method. In addition, several slot antennas and horn antennas fabricated using the SIW technology are also given. Table of Contents: Introduction / SIW Circuits Composed of Metallic Posts / SIW Circuits with Dielectric Posts / Even-Odd Mode Analysis of a Symmetrical Circuit / Microstrip to SIW Transition and Half Mode SIW / SIW Antennas
Book Synopsis Multiresolution Frequency Domain Technique for Electromagnetics by : Mesut Gökten
Download or read book Multiresolution Frequency Domain Technique for Electromagnetics written by Mesut Gökten and published by Springer Nature. This book was released on 2022-06-01 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, a general frequency domain numerical method similar to the finite difference frequency domain (FDFD) technique is presented. The proposed method, called the multiresolution frequency domain (MRFD) technique, is based on orthogonal Battle-Lemarie and biorthogonal Cohen-Daubechies-Feauveau (CDF) wavelets. The objective of developing this new technique is to achieve a frequency domain scheme which exhibits improved computational efficiency figures compared to the traditional FDFD method: reduced memory and simulation time requirements while retaining numerical accuracy. The newly introduced MRFD scheme is successfully applied to the analysis of a number of electromagnetic problems, such as computation of resonance frequencies of one and three dimensional resonators, analysis of propagation characteristics of general guided wave structures, and electromagnetic scattering from two dimensional dielectric objects. The efficiency characteristics of MRFD techniques based on different wavelets are compared to each other and that of the FDFD method. Results indicate that the MRFD techniques provide substantial savings in terms of execution time and memory requirements, compared to the traditional FDFD method. Table of Contents: Introduction / Basics of the Finite Difference Method and Multiresolution Analysis / Formulation of the Multiresolution Frequency Domain Schemes / Application of MRFD Formulation to Closed Space Structures / Application of MRFD Formulation to Open Space Structures / A Multiresolution Frequency Domain Formulation for Inhomogeneous Media / Conclusion
Book Synopsis Selected Asymptotic Methods with Applications to Electromagnetics and Antennas by : George Fikioris
Download or read book Selected Asymptotic Methods with Applications to Electromagnetics and Antennas written by George Fikioris and published by Springer Nature. This book was released on 2022-06-01 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include some recent, direct applications to antennas and computational electromagnetics. Then, specific methods are discussed. These include integration by parts and the Riemann-Lebesgue lemma, the use of contour integration in conjunction with other methods, techniques related to Laplace's method and Watson's lemma, the asymptotic behavior of certain Fourier sine and cosine transforms, and the Poisson summation formula (including its version for finite sums). Often underutilized in the literature are asymptotic techniques based on the Mellin transform; our treatment of this subject complements the techniques presented in our recent Synthesis Lecture on the exact (not asymptotic) evaluation of integrals.
Book Synopsis An Introduction to the Locally Corrected Nystrom Method by : Andrew Peterson
Download or read book An Introduction to the Locally Corrected Nystrom Method written by Andrew Peterson and published by Springer Nature. This book was released on 2022-05-31 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture provides a tutorial introduction to the Nyström and locally-corrected Nyström methods when used for the numerical solutions of the common integral equations of two-dimensional electromagnetic fields. These equations exhibit kernel singularities that complicate their numerical solution. Classical and generalized Gaussian quadrature rules are reviewed. The traditional Nyström method is summarized, and applied to the magnetic field equation for illustration. To obtain high order accuracy in the numerical results, the locally-corrected Nyström method is developed and applied to both the electric field and magnetic field equations. In the presence of target edges, where current or charge density singularities occur, the method must be extended through the use of appropriate singular basis functions and special quadrature rules. This extension is also described. Table of Contents: Introduction / Classical Quadrature Rules / The Classical Nyström Method / The Locally-Corrected Nyström Method / Generalized Gaussian Quadrature / LCN Treatment of Edge Singularities
Book Synopsis Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects by : Erdogan Alkan
Download or read book Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects written by Erdogan Alkan and published by Springer Nature. This book was released on 2022-05-31 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid (DG-FDFD) approach for general bianisotropic materials. The validity of the derived formulations for different scattering problems has been shown by comparing the obtained results to exact and other solutions obtained using different numerical methods. Table of Contents: Introduction / Chiral Media / Basics of the Finite-Difference Frequency-Domain (FDFD) Method / The Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Bianisotropic Medium / Scattering FromThree Dimensional Chiral Structures / ImprovingTime and Memory Efficiencies of FDFD Methods / Conclusions / Appendix A: Notations / Appendix B: Near to Far FieldTransformation
Book Synopsis Scattering Analysis of Periodic Structures using Finite-Difference Time-Domain Method by : Khaled ElMahgoub
Download or read book Scattering Analysis of Periodic Structures using Finite-Difference Time-Domain Method written by Khaled ElMahgoub and published by Springer Nature. This book was released on 2022-06-01 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Periodic structures are of great importance in electromagnetics due to their wide range of applications such as frequency selective surfaces (FSS), electromagnetic band gap (EBG) structures, periodic absorbers, meta-materials, and many others. The aim of this book is to develop efficient computational algorithms to analyze the scattering properties of various electromagnetic periodic structures using the finite-difference time-domain periodic boundary condition (FDTD/PBC) method. A new FDTD/PBC-based algorithm is introduced to analyze general skewed grid periodic structures while another algorithm is developed to analyze dispersive periodic structures. Moreover, the proposed algorithms are successfully integrated with the generalized scattering matrix (GSM) technique, identified as the hybrid FDTD-GSM algorithm, to efficiently analyze multilayer periodic structures. All the developed algorithms are easy to implement and are efficient in both computational time and memory usage. These algorithms are validated through several numerical test cases. The computational methods presented in this book will help scientists and engineers to investigate and design novel periodic structures and to explore other research frontiers in electromagnetics. Table of Contents: Introduction / FDTD Method and Periodic Boundary Conditions / Skewed Grid Periodic Structures / Dispersive Periodic Structures / Multilayered Periodic Structures / Conclusions
Book Synopsis Integral Equation Methods in Scattering Theory by : David Colton
Download or read book Integral Equation Methods in Scattering Theory written by David Colton and published by SIAM. This book was released on 2013-11-15 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.