Support Vector Machines for Antenna Array Processing and Electromagnetics

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Publisher : Morgan & Claypool Publishers
ISBN 13 : 159829024X
Total Pages : 121 pages
Book Rating : 4.5/5 (982 download)

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Book Synopsis Support Vector Machines for Antenna Array Processing and Electromagnetics by : Manel Martínez-Ramón

Download or read book Support Vector Machines for Antenna Array Processing and Electromagnetics written by Manel Martínez-Ramón and published by Morgan & Claypool Publishers. This book was released on 2006 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the 1990s there has been significant activity in the theoretical development and applications of Support Vector Machines (SVMs). The theory of SVMs is based on the cross-pollenization of optimization theory, statistical learning, kernel theory, and algorithmics. So far, machine learning has largely been devoted to solving problems relating to data mining, text categorization, and pattern/facial recognition but not so much in the field of electromagnetics. Recently, however, popular binary machine learning algorithms, including support vector machines (SVM), have successfully been applied to wireless communication problems, notably spread spectrum receiver design and channelequalization.The aim of this book is to gently introduce support vector machines in its linear and non linear form, both as regressors and as classifiers, and to show how they can be applied to several antenna array processing problems and electromagnetics in general.The lecture is divided into three main parts. The first three chapters cover the theory of SVMS, both as classifiers and regressors. The next three chapters deal with applications in antenna array processing and other areas in electromagnetics. The four appendices at the end of the book comprise the last part. The inclusion of MATLAB files will help readers start their application of the algorithms covered in the book.

Support Vector Machines for Antenna Array Processing and Electromagnetics

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Author :
Publisher : Springer Nature
ISBN 13 : 3031016920
Total Pages : 110 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Support Vector Machines for Antenna Array Processing and Electromagnetics by : Manel Martínez-Ramón

Download or read book Support Vector Machines for Antenna Array Processing and Electromagnetics written by Manel Martínez-Ramón and published by Springer Nature. This book was released on 2022-06-01 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Support Vector Machines (SVM) were introduced in the early 90's as a novel nonlinear solution for classification and regression tasks. These techniques have been proved to have superior performances in a large variety of real world applications due to their generalization abilities and robustness against noise and interferences. This book introduces a set of novel techniques based on SVM that are applied to antenna array processing and electromagnetics. In particular, it introduces methods for linear and nonlinear beamforming and parameter design for arrays and electromagnetic applications.

Support Vector Machines for Antenna Array Processing and Electromagnetics

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Publisher :
ISBN 13 : 9788303101693
Total Pages : 0 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Support Vector Machines for Antenna Array Processing and Electromagnetics by : Christos Christodoulou

Download or read book Support Vector Machines for Antenna Array Processing and Electromagnetics written by Christos Christodoulou and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Support Vector Machines (SVM) were introduced in the early 90's as a novel nonlinear solution for classification and regression tasks. These techniques have been proved to have superior performances in a large variety of real world applications due to their generalization abilities and robustness against noise and interferences. This book introduces a set of novel techniques based on SVM that are applied to antenna array processing and electromagnetics. In particular, it introduces methods for linear and nonlinear beamforming and parameter design for arrays and electromagnetic applications.

Machine Learning Applications in Electromagnetics and Antenna Array Processing

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Publisher : Artech House
ISBN 13 : 1630817767
Total Pages : 436 pages
Book Rating : 4.6/5 (38 download)

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Book Synopsis Machine Learning Applications in Electromagnetics and Antenna Array Processing by : Manel Martínez-Ramón

Download or read book Machine Learning Applications in Electromagnetics and Antenna Array Processing written by Manel Martínez-Ramón and published by Artech House. This book was released on 2021-04-30 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical resource provides an overview of machine learning (ML) approaches as applied to electromagnetics and antenna array processing. Detailed coverage of the main trends in ML, including uniform and random array processing (beamforming and detection of angle of arrival), antenna optimization, wave propagation, remote sensing, radar, and other aspects of electromagnetic design are explored. An introduction to machine learning principles and the most common machine learning architectures and algorithms used today in electromagnetics and other applications is presented, including basic neural networks, gaussian processes, support vector machines, kernel methods, deep learning, convolutional neural networks, and generative adversarial networks. Applications in electromagnetics and antenna array processing that are solved using machine learning are discussed, including antennas, remote sensing, and target classification.

Advances in Electromagnetics Empowered by Artificial Intelligence and Deep Learning

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Publisher : John Wiley & Sons
ISBN 13 : 1119853915
Total Pages : 596 pages
Book Rating : 4.1/5 (198 download)

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Book Synopsis Advances in Electromagnetics Empowered by Artificial Intelligence and Deep Learning by : Sawyer D. Campbell

Download or read book Advances in Electromagnetics Empowered by Artificial Intelligence and Deep Learning written by Sawyer D. Campbell and published by John Wiley & Sons. This book was released on 2023-08-03 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Electromagnetics Empowered by Artificial Intelligence and Deep Learning Authoritative reference on the state of the art in the field with additional coverage of important foundational concepts Advances in Electromagnetics Empowered by Artificial Intelligence and Deep Learning presents cutting-edge research advances in the rapidly growing areas in optical and RF electromagnetic device modeling, simulation, and inverse-design. The text provides a comprehensive treatment of the field on subjects ranging from fundamental theoretical principles and new technological developments to state-of-the-art device design, as well as examples encompassing a wide range of related sub-areas. The content of the book covers all-dielectric and metallodielectric optical metasurface deep learning-accelerated inverse-design, deep neural networks for inverse scattering, applications of deep learning for advanced antenna design, and other related topics. To aid in reader comprehension, each chapter contains 10-15 illustrations, including prototype photos, line graphs, and electric field plots. Contributed to by leading research groups in the field, sample topics covered in Advances in Electromagnetics Empowered by Artificial Intelligence and Deep Learning include: Optical and photonic design, including generative machine learning for photonic design and inverse design of electromagnetic systems RF and antenna design, including artificial neural networks for parametric electromagnetic modeling and optimization and analysis of uniform and non-uniform antenna arrays Inverse scattering, target classification, and other applications, including deep learning for high contrast inverse scattering of electrically large structures Advances in Electromagnetics Empowered by Artificial Intelligence and Deep Learning is a must-have resource on the topic for university faculty, graduate students, and engineers within the fields of electromagnetics, wireless communications, antenna/RF design, and photonics, as well as researchers at large defense contractors and government laboratories.

Ultra-Wideband Short-Pulse Electromagnetics 8

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Publisher : Springer Science & Business Media
ISBN 13 : 038773046X
Total Pages : 268 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Ultra-Wideband Short-Pulse Electromagnetics 8 by : Carl E. Baum

Download or read book Ultra-Wideband Short-Pulse Electromagnetics 8 written by Carl E. Baum and published by Springer Science & Business Media. This book was released on 2007-12-05 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the Ultra-Wideband Short-Pulse Electromagnetics Conference series is to focus on advanced technologies for the generation, radiation and detection of ultra-wideband short pulse signals, taking into account their propagation and scattering from and coupling to targets of interest. This Conference series reports on developments in supporting mathematical and numerical methods and presents current and potential future applications of the technology. Ultra-Wideband Short-Pulse Electromagnetics 8 is based on the American Electromagnetics 2006 conference held from June 3-7 in Albuquerque, New Mexico. Topical areas covered in this volume include pulse radiation and measurement, scattering theory, target detection and identification, antennas, signal processing, and communications.

Encyclopedia of Data Warehousing and Mining, Second Edition

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Publisher : IGI Global
ISBN 13 : 1605660116
Total Pages : 2542 pages
Book Rating : 4.6/5 (56 download)

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Book Synopsis Encyclopedia of Data Warehousing and Mining, Second Edition by : Wang, John

Download or read book Encyclopedia of Data Warehousing and Mining, Second Edition written by Wang, John and published by IGI Global. This book was released on 2008-08-31 with total page 2542 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are more than one billion documents on the Web, with the count continually rising at a pace of over one million new documents per day. As information increases, the motivation and interest in data warehousing and mining research and practice remains high in organizational interest. The Encyclopedia of Data Warehousing and Mining, Second Edition, offers thorough exposure to the issues of importance in the rapidly changing field of data warehousing and mining. This essential reference source informs decision makers, problem solvers, and data mining specialists in business, academia, government, and other settings with over 300 entries on theories, methodologies, functionalities, and applications.

Soft Computing Methods for Microwave and Millimeter-Wave Design Problems

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Publisher : Springer Science & Business Media
ISBN 13 : 3642255620
Total Pages : 119 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Soft Computing Methods for Microwave and Millimeter-Wave Design Problems by : Narendra Chauhan

Download or read book Soft Computing Methods for Microwave and Millimeter-Wave Design Problems written by Narendra Chauhan and published by Springer Science & Business Media. This book was released on 2012-02-09 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: The growing commercial market of Microwave/ Millimeter wave industry over the past decade has led to the explosion of interests and opportunities for the design and development of microwave components.The design of most microwave components requires the use of commercially available electromagnetic (EM) simulation tools for their analysis. In the design process, the simulations are carried out by varying the design parameters until the desired response is obtained. The optimization of design parameters by manual searching is a cumbersome and time consuming process. Soft computing methods such as Genetic Algorithm (GA), Artificial Neural Network (ANN) and Fuzzy Logic (FL) have been widely used by EM researchers for microwave design since last decade. The aim of these methods is to tolerate imprecision, uncertainty, and approximation to achieve robust and low cost solution in a small time frame. Modeling and optimization are essential parts and powerful tools for the microwave/millimeter wave design. This book deals with the development and use of soft computing methods for tackling challenging design problems in the microwave/millimeter wave domain. The aim in the development of these methods is to obtain the design in small time frame while improving the accuracy of the design for a wide range of applications. To achieve this goal, a few diverse design problems of microwave field, representing varied challenges in the design, such as different microstrip antennas, microwave filters, a microstrip-via and also some critical high power components such as nonlinear tapers and RF-windows are considered as case-study design problems. Different design methodologies are developed for these applications. The presents soft computing methods, their review for microwave/millimeter wave design problems and specific case-study problems to infuse better insight and understanding of the subject.

Selected Asymptotic Methods with Applications to Electromagnetics and Antennas

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Publisher : Springer Nature
ISBN 13 : 3031017161
Total Pages : 187 pages
Book Rating : 4.0/5 (31 download)

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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.

Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics

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Publisher : Springer Nature
ISBN 13 : 3031017129
Total Pages : 242 pages
Book Rating : 4.0/5 (31 download)

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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

Kernel Methods in Bioengineering, Signal and Image Processing

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Publisher : IGI Global
ISBN 13 : 1599040425
Total Pages : 431 pages
Book Rating : 4.5/5 (99 download)

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Book Synopsis Kernel Methods in Bioengineering, Signal and Image Processing by : Gustavo Camps-Valls

Download or read book Kernel Methods in Bioengineering, Signal and Image Processing written by Gustavo Camps-Valls and published by IGI Global. This book was released on 2007-01-01 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents an extensive introduction to the field of kernel methods and real world applications. The book is organized in four parts: the first is an introductory chapter providing a framework of kernel methods; the others address Bioegineering, Signal Processing and Communications and Image Processing"--Provided by publisher.

Future Trends in 5G and 6G

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Publisher : CRC Press
ISBN 13 : 1000504069
Total Pages : 357 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Future Trends in 5G and 6G by : Mangesh M. Ghonge

Download or read book Future Trends in 5G and 6G written by Mangesh M. Ghonge and published by CRC Press. This book was released on 2021-12-30 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive overview of basic communication and networking technologies. It focuses on emerging technologies, such as Software-Defined Network (SDN)-based ad hoc networks, 5G, Machine Learning, and Deep Learning solutions for communication and networking, Cloud Computing, etc. It also includes discussions on practical and innovative applications, including Network Security, Smart Cities, e-health, and Intelligent Systems. Future Trends in 5G and 6G: Challenges, Architecture, and Applications addresses several key issues in SDN energy-efficient systems, the Internet of Things, Big Data, Cloud Computing and Virtualization, Machine Learning, Deep Learning, Cryptography, and 6G wireless technology and its future. It provides students, researchers, and practicing engineers with an expert guide to the fundamental concepts, challenges, architecture, applications, and state-of-the-art developments in communication and networking.

Social Media and Crowdsourcing

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Publisher : CRC Press
ISBN 13 : 1003804861
Total Pages : 259 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Social Media and Crowdsourcing by : Sujoy Chatterjee

Download or read book Social Media and Crowdsourcing written by Sujoy Chatterjee and published by CRC Press. This book was released on 2023-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Social media and crowdsourcing are important tools for solving complex problems. The benefit of crowdsourcing is that it leverages the power of human intelligence cost effectively and with less time. Social Media and Crowdsourcing: Application and Analytics examines the concepts of social media and crowdsourcing as well as their analytical aspects. It explores how these technologies contribute to the real world and examines such applications as promoting social good, agriculture, healthcare, tourism, disaster management, education, crime control, and cultural heritage. The book also looks at ethical issues in crowdsourcing and future scenarios and challenges for policy. Highlights of the book include the following: A crowdsourcing application in agriculture Crowdsourcing outline for a contemporary aided medicinal backup system Crowdsourcing-based recommendation in the tourism industry Crowdsourcing mechanisms for reviving cultural heritage Expanding the overarching concept of utilizing social media and crowdsourcing to solve various real-life problems, this book discusses how to bring together the wisdom of crowds for various decision-making problems in agriculture, disaster management, and healthcare. It addresses the various ethical issues arising out of various crowdsourcing-based applications. It puts forward diverse methodologies to involve crowdsourcing in education to implement new strategies to enhance learning outcomes. This book also addresses various problem-solving techniques for recommender applications in the travel and tourism industry. Providing a systematic discussion of the many sectors using crowdsourcing as an essential part of social innovation, this book is a theoretical and methodological look at the application of social media.

Analysis and Design of Substrate Integrated Waveguide Using Efficient 2D Hybrid Method

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Publisher : Springer Nature
ISBN 13 : 3031017110
Total Pages : 82 pages
Book Rating : 4.0/5 (31 download)

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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

Simulation-driven Design Optimization And Modeling For Microwave Engineering

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Publisher : World Scientific
ISBN 13 : 1848169221
Total Pages : 526 pages
Book Rating : 4.8/5 (481 download)

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Book Synopsis Simulation-driven Design Optimization And Modeling For Microwave Engineering by : Qi-jun Zhang

Download or read book Simulation-driven Design Optimization And Modeling For Microwave Engineering written by Qi-jun Zhang and published by World Scientific. This book was released on 2013-03-14 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer-aided full-wave electromagnetic (EM) analysis has been used in microwave engineering for the past decade. Initially, its main application area was design verification. Today, EM-simulation-driven optimization and design closure become increasingly important due to the complexity of microwave structures and increasing demands for accuracy. In many situations, theoretical models of microwave structures can only be used to yield the initial designs that need to be further fine-tuned to meet given performance requirements. In addition, EM-based design is a must for a growing number of microwave devices such as ultra-wideband (UWB) antennas, dielectric resonator antennas and substrate-integrated circuits. For circuits like these, no design-ready theoretical models are available, so design improvement can only be obtained through geometry adjustments based on repetitive, time-consuming simulations. On the other hand, various interactions between microwave devices and their environment, such as feeding structures and housing, must be taken into account, and this is only possible through full-wave EM analysis.Electromagnetic simulations can be highly accurate, but they tend to be computationally expensive. Therefore, practical design optimization methods have to be computationally efficient, so that the number of CPU-intensive high-fidelity EM simulations is reduced as much as possible during the design process. For the same reasons, techniques for creating fast yet accurate models of microwave structures become crucially important.In this edited book, the authors strive to review the state-of-the-art simulation-driven microwave design optimization and modeling. A group of international experts specialized in various aspects of microwave computer-aided design summarize and review a wide range of the latest developments and real-world applications. Topics include conventional and surrogate-based design optimization techniques, methods exploiting adjoint sensitivity, simulation-based tuning, space mapping, and several modeling methodologies, such as artificial neural networks and kriging. Applications and case studies include microwave filters, antennas, substrate integrated structures and various active components and circuits. The book also contains a few introductory chapters highlighting the fundamentals of optimization and modeling, gradient-based and derivative-free algorithms, metaheuristics, and surrogate-based optimization techniques, as well as finite difference and finite element methods./a

Accurate Computation of Mathieu Functions

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Publisher : Springer Nature
ISBN 13 : 303101717X
Total Pages : 123 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Accurate Computation of Mathieu Functions by : Andrew Peterson

Download or read book Accurate Computation of Mathieu Functions written by Andrew Peterson and published by Springer Nature. This book was released on 2022-06-01 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture presents a modern approach for the computation of Mathieu functions. These functions find application in boundary value analysis such as electromagnetic scattering from elliptic cylinders and flat strips, as well as the analogous acoustic and optical problems, and many other applications in science and engineering. The authors review the traditional approach used for these functions, show its limitations, and provide an alternative "tuned" approach enabling improved accuracy and convergence. The performance of this approach is investigated for a wide range of parameters and machine precision. Examples from electromagnetic scattering are provided for illustration and to show the convergence of the typical series that employ Mathieu functions for boundary value analysis.

Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects

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Publisher : Springer Nature
ISBN 13 : 3031017153
Total Pages : 119 pages
Book Rating : 4.0/5 (31 download)

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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