Adaptive Mesh Refinement In Time Domain Numerical Electromagnetics

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Adaptive Mesh Refinement for Time-domain Numerical Electromagnetics

Author : Costas D. Sarris
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1598290789
Total Pages : 154 pages
Book Rating : 4.5/5 (982 download)

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Book Synopsis Adaptive Mesh Refinement for Time-domain Numerical Electromagnetics by : Costas D. Sarris

Download or read book Adaptive Mesh Refinement for Time-domain Numerical Electromagnetics written by Costas D. Sarris and published by Morgan & Claypool Publishers. This book was released on 2007 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Therefore, they are excellent computer analysis and design (CAD) tools. The book starts by introducing the FDTD technique, along with challenges related to its application to the analysis of real-life microwave and optical structures. It then proceeds to developing an adaptive mesh refinement method based on the use of multiresolution analysis and, more specifically, the Haar wavelet basis. Furthermore, a new method to embed a moving adaptive mesh in FDTD, the dynamically adaptive mesh refinement (AMR) FDTD technique, is introduced and explained in detail. To highlight the properties of the theoretical tools developed in the text, a number of applications are presented, including: Microwave integrated circuits (microstrip filters, couplers, spiral inductors, cavities); Optical power splitters, Y-junctions, and couplers; Optical ring resonators; Nonlinear optical waveguides.

Adaptive Mesh Refinement in Time-Domain Numerical Electromagnetics

Author : Costas Sarris
Publisher : Springer Nature
ISBN 13 : 3031016955
Total Pages : 135 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Adaptive Mesh Refinement in Time-Domain Numerical Electromagnetics by : Costas Sarris

Download or read book Adaptive Mesh Refinement in Time-Domain Numerical Electromagnetics written by Costas Sarris and published by Springer Nature. This book was released on 2022-05-31 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a comprehensive presentation of state-of-the-art methodologies that can dramatically enhance the efficiency of the finite-difference time-domain (FDTD) technique, the most popular electromagnetic field solver of the time-domain form of Maxwell's equations. These methodologies are aimed at optimally tailoring the computational resources needed for the wideband simulation of microwave and optical structures to their geometry, as well as the nature of the field solutions they support. That is achieved by the development of robust “adaptive meshing” approaches, which amount to varying the total number of unknown field quantities in the course of the simulation to adapt to temporally or spatially localized field features. While mesh adaptation is an extremely desirable FDTD feature, known to reduce simulation times by orders of magnitude, it is not always robust. The specific techniques presented in this book are characterized by stability and robustness. Therefore, they are excellent computer analysis and design (CAD) tools. The book starts by introducing the FDTD technique, along with challenges related to its application to the analysis of real-life microwave and optical structures. It then proceeds to developing an adaptive mesh refinement method based on the use of multiresolution analysis and, more specifically, the Haar wavelet basis. Furthermore, a new method to embed a moving adaptive mesh in FDTD, the dynamically adaptive mesh refinement (AMR) FDTD technique, is introduced and explained in detail. To highlight the properties of the theoretical tools developed in the text, a number of applications are presented, including: Microwave integrated circuits (microstrip filters, couplers, spiral inductors, cavities). Optical power splitters, Y-junctions, and couplers Optical ring resonators Nonlinear optical waveguides. Building on first principles of time-domain electromagnetic simulations, this book presents advanced concepts and cutting-edge modeling techniques in an intuitive way for programmers, engineers, and graduate students. It is designed to provide a solid reference for highly efficient time-domain solvers, employed in a wide range of exciting applications in microwave/millimeter-wave and optical engineering.

Numerical Electromagnetics

Author : Umran S. Inan
Publisher : Cambridge University Press
ISBN 13 : 1139497987
Total Pages : 405 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Numerical Electromagnetics by : Umran S. Inan

Download or read book Numerical Electromagnetics written by Umran S. Inan and published by Cambridge University Press. This book was released on 2011-04-07 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with the development of finite difference equations, and leading to the complete FDTD algorithm, this is a coherent introduction to the FDTD method (the method of choice for modeling Maxwell's equations). It provides students and professional engineers with everything they need to know to begin writing FDTD simulations from scratch and to develop a thorough understanding of the inner workings of commercial FDTD software. Stability, numerical dispersion, sources and boundary conditions are all discussed in detail, as are dispersive and anisotropic materials. A comparative introduction of the finite volume and finite element methods is also provided. All concepts are introduced from first principles, so no prior modeling experience is required, and they are made easier to understand through numerous illustrative examples and the inclusion of both intuitive explanations and mathematical derivations.

Adaptive Mesh Refinement - Theory and Applications

Author : Tomasz Plewa
Publisher : Springer Science & Business Media
ISBN 13 : 9783540211471
Total Pages : 582 pages
Book Rating : 4.2/5 (114 download)

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Book Synopsis Adaptive Mesh Refinement - Theory and Applications by : Tomasz Plewa

Download or read book Adaptive Mesh Refinement - Theory and Applications written by Tomasz Plewa and published by Springer Science & Business Media. This book was released on 2004-12-08 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.

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

Author : Stephen Gedney
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

Scattering Analysis of Periodic Structures using Finite-Difference Time-Domain Method

Author : Khaled ElMahgoub
Publisher : Springer Nature
ISBN 13 : 3031017137
Total Pages : 122 pages
Book Rating : 4.0/5 (31 download)

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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

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

Author : Xuan Hui Wu
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

Selected Asymptotic Methods with Applications to Electromagnetics and Antennas

Author : George Fikioris
Publisher : Morgan & Claypool Publishers
ISBN 13 : 162705040X
Total Pages : 209 pages
Book Rating : 4.6/5 (27 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 Morgan & Claypool Publishers. This book was released on 2013-09-01 with total page 209 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.

Adaptive Mesh Refinement - Theory and Applications

Author : Tomasz Plewa
Publisher : Springer
ISBN 13 : 9783540801092
Total Pages : 554 pages
Book Rating : 4.8/5 (1 download)

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Book Synopsis Adaptive Mesh Refinement - Theory and Applications by : Tomasz Plewa

Download or read book Adaptive Mesh Refinement - Theory and Applications written by Tomasz Plewa and published by Springer. This book was released on 2009-09-02 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.

Adaptive Mesh Refinement for Pseudospectral Methods in Numerical Relativity

Author : Sarah Renkhoff
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (143 download)

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Book Synopsis Adaptive Mesh Refinement for Pseudospectral Methods in Numerical Relativity by : Sarah Renkhoff

Download or read book Adaptive Mesh Refinement for Pseudospectral Methods in Numerical Relativity written by Sarah Renkhoff and published by . This book was released on 2023* with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Across all of computational physics, a central problem is that of discretization, from the choice of resolution in simple finite difference approaches, to the details of more intricate discretization schemes such as spectral elements. The choice of discretization decides the numerical solution space, as well as the properties of numerical methods, such as their convergence and stability. For this reason, the effective use of any numerical scheme requires a proper understanding of the underlying discretization scheme and its parameters. In particular, modern numerical methods often incorporate adaptive discretization schemes, utilizing heterogeneous meshes that change with time. In this work, we will explore one such method in the form of a state-of-the-art numerical relativity code, and the implementation of an adaptive mesh refinement (AMR) scheme within it. We describe in detail its features, and the resulting properties as it is used to solve physical problems in the form of hyperbolic partial differential equations, and we examine the scaling behavior of the resulting method. We also present results obtained using this scheme, in the form of simulations of the critical collapse of gravitational waves, that were made possible by the AMR system, showing some evidence of both self-similarity and universality in this system. Finally, we study a suite of several challenging test cases, beginning with a simple two-dimensional wave equation with an added nonlinearity, which results in critical behavior for certain choices of initial data, then moving on to the collapse of a real scalar field minimally coupled to general relativity in spherical symmetry. Finally, we use the collapse of gravitational waves in vacuum in axisymmetry as our third test case. We use these example problems to evaluate the gains in terms of accuracy, as well as efficiency, that are obtained through the use of adaptive resolutions.

Boundary Elements and Other Mesh Reduction Methods Twenty-eight

Author : C. A. Brebbia
Publisher : WIT Press
ISBN 13 : 1845641647
Total Pages : 361 pages
Book Rating : 4.8/5 (456 download)

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Book Synopsis Boundary Elements and Other Mesh Reduction Methods Twenty-eight by : C. A. Brebbia

Download or read book Boundary Elements and Other Mesh Reduction Methods Twenty-eight written by C. A. Brebbia and published by WIT Press. This book was released on 2006 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers from the World Conference on Boundary Elements and other Mesh Reduction Methods, an internationally recognized forum for the dissemination of the latest advances on Mesh Reduction Techniques and their applications in sciences and engineering. The book publishes articles dealing with computational issues and software developments in addition to those of a more theoretical nature. Engineers and scientists within the areas of numerical analysis, boundary elements and meshless methods will find the text invaluable. Topics include: Advances in Mesh Reduction Methods; Meshless Techniques; Advanced Formulations; Dual Reciprocity Method; Modified Trefftz Method; Fundamental Solution Method; Damage Mechanics and Fracture; Advanced Structural Applications; Dynamics and Vibrations; Material Characterization; Acoustics; Electrical Engineering and Electromagnetics; Heat and Mass Transfer; Fluid Mechanics Problems; Wave Propagation; Inverse Problems and Computational Techniques.

Advances in Computational Electrodynamics

Author : Allen Taflove
Publisher : Artech House Publishers
ISBN 13 :
Total Pages : 766 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Advances in Computational Electrodynamics by : Allen Taflove

Download or read book Advances in Computational Electrodynamics written by Allen Taflove and published by Artech House Publishers. This book was released on 1998 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite-Difference Time-Domain (FD-TD) modeling is arguably the most popular and powerful means available to perform detailed electromagnetic engineering analyses. Edited by the pioneer and foremost authority on the subject, here is the first book to assemble in one resource the latest techniques and results of the leading theoreticians and practitioners of FD-TD computational electromagnetics modeling.

MRTD (Multi Resolution Time Domain) Method in Electromagnetics

Author : Nathan Bushyager
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1598290150
Total Pages : 116 pages
Book Rating : 4.5/5 (982 download)

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Book Synopsis MRTD (Multi Resolution Time Domain) Method in Electromagnetics by : Nathan Bushyager

Download or read book MRTD (Multi Resolution Time Domain) Method in Electromagnetics written by Nathan Bushyager and published by Morgan & Claypool Publishers. This book was released on 2006-12-01 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a method that allows the use of multiresolution principles in a time domain electromagnetic modeling technique that is applicable to general structures. The multiresolution time-domain (MRTD) technique, as it is often called, is presented for general basis functions. Additional techniques that are presented here allow the modeling of complex structures using a subcell representation that permits the modeling discrete electromagnetic effects at individual equivalent grid points. This is accomplished by transforming the application of the effects at individual points in the grid into the wavelet domain. In this work, the MRTD technique is derived for a general wavelet basis using a relatively compact vector notation that both makes the technique easier to understand and illustrates the differences between MRTD basis functions. In addition, techniques such as the uniaxial perfectly matched layer (UPML) for arbitrary wavelet resolution and non-uniform gridding are presented. Using these techniques, any structure that can be simulated in Yee-FDTD can be modeled with in MRTD.

Efficient Solution of Maxwell's Equations Using the Nonuniform Orthogonal Finite Difference Time Domain Method

Author : John Allan Svigelj
Publisher :
ISBN 13 :
Total Pages : 306 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Efficient Solution of Maxwell's Equations Using the Nonuniform Orthogonal Finite Difference Time Domain Method by : John Allan Svigelj

Download or read book Efficient Solution of Maxwell's Equations Using the Nonuniform Orthogonal Finite Difference Time Domain Method written by John Allan Svigelj and published by . This book was released on 1995 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Finite Difference Time Domain (FDTD) method is limited by memory requirements and computation time when applied to large problems, complicated geometries, or geometries with fine features. In this thesis, the nonuniform orthogonal FDTD method is presented and applied to a variety of electromagnetic problems. The nonuniform aspect of the method gives great flexibility in modeling complicated geometries with fine features. Furthermore, the variability of the mesh resolution also enables the user to move the boundaries of the computational domain farther away from the center of the problem without an undue increase in the number of cells. Most significantly, the orthogonality of the method preserves the speed of the conventional FDTD method. These three features of the nonuniform orthogonal FDTD method are demonstrated by means of numerical examples throughout the thesis. Grid dispersion error from the nonuniform mesh is analyzed and numerical examples are presented, demonstrating that small growth rates in mesh discretization lead to acceptably small errors. The issue of absorbing boundary conditions is addressed with the analysis and application of the dispersive boundary condition on nonuniform meshes. New techniques are also introduced for the efficient characterization of microstrip lines, microstrip discontinuities, and coupled microstrip structures using FDTD data. A local mesh refinement technique is introduced for planar perfect electric conductor, and is shown to be three times more accurate than the staircasing approximation. The versatility of the method is demonstrated by the analysis of a balun-fed folded dipole antenna, the characterization of the transition of grounded coplanar waveguide to microstrip line, and the study of fields in lossy layered media.

Computational Electrodynamics

Author : Allen Taflove
Publisher : Artech House Publishers
ISBN 13 :
Total Pages : 1050 pages
Book Rating : 4.3/5 (21 download)

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Book Synopsis Computational Electrodynamics by : Allen Taflove

Download or read book Computational Electrodynamics written by Allen Taflove and published by Artech House Publishers. This book was released on 2005 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: This extensively revised and expanded third edition of the Artech House bestseller, Computational Electrodynamics: The Finite-Difference Time-Domain Method, offers you the most up-to-date and definitive resource on this critical method for solving Maxwell's equations. There has been considerable advancement in FDTD computational technology over the past few years, and this new edition brings you the very latest details with four new invited chapters on advanced techniques for PSTD, unconditional stability, provably stable FDTD-FETD hybrids, and hardware acceleration. Moreover, you find many completely new sections throughout the book, including major updates on convolutional PML ABCs; dispersive, nonlinear, classical-gain, and quantum-gain materials; and micro-, nano-, and bio- photonics.

The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB® Simulations

Author : Atef Z. Elsherbeni
Publisher : IET
ISBN 13 : 1613531753
Total Pages : 559 pages
Book Rating : 4.6/5 (135 download)

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Book Synopsis The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB® Simulations by : Atef Z. Elsherbeni

Download or read book The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB® Simulations written by Atef Z. Elsherbeni and published by IET. This book was released on 2015-11-25 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is one of the best books on computational electromagnetics both for graduate students focusing on electromagnetics problems and for practicing engineering professionals in industry and government. It is designed as an advanced textbook and self-study guide to the FDTD method of solving EM problems and simulations. This latest edition has been expanded to include 5 entirely new chapters on advanced topics in the mainstream of FDTD practice. In addition to advanced techniques it also includes applications and examples, and some 'tricks and traps' of using MATLAB to achieve them. Compared to the previous version the second edition is more complete and is a good reference for someone who is performing FDTD research. This book is part of the ACES Series on Computational Electromagnetics and Engineering. Supplementary material can be found at the IET's ebook page Supplementary materials for professors are available upon request via email to [email protected].

High Order Difference Methods for Time Dependent PDE

Author : Bertil Gustafsson
Publisher : Springer Science & Business Media
ISBN 13 : 3540749934
Total Pages : 343 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis High Order Difference Methods for Time Dependent PDE by : Bertil Gustafsson

Download or read book High Order Difference Methods for Time Dependent PDE written by Bertil Gustafsson and published by Springer Science & Business Media. This book was released on 2007-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers high order finite difference methods for time dependent PDE. It gives an overview of the basic theory and construction principles by using model examples. The book also contains a general presentation of the techniques and results for well-posedness and stability, with inclusion of the three fundamental methods of analysis both for PDE in its original and discretized form: the Fourier transform, the eneregy method and the Laplace transform.