Time Domain Simulation of Maxwell's Equations by the Method of Characteristics PDF Download
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Author: Neven Orhanović
Publisher:
ISBN:
Category : Maxwell equations
Languages : en
Pages : 180
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Book Description
A numerical method based on the the method of characteristics for hyperbolic systems of partial differential equations in four independent variables is developed and used for solving time domain Maxwell's equations. The method uses the characteristic hypersurfaces and the characteristic conditions to derive a set of independent equations relating the electric and magnetic field components on these hypersurfaces. A discretization scheme is developed to solve for the unknown field components at each time step. The method retains many of the good features of the original method of characteristics for hyperbolic systems in two independent variables, such as optimal time step, good behavior near data discontinuities and the ability to treat general boundary conditions. The method is exemplified by calculating the time domain response of a few typical planar interconnect structures to Gaussian and unit step excitations. Although the general emphasis is on interconnect problems, the method is applicable to a number of other transient electromagnetic field problems governed by Maxwell's equations. In addition to the method of characteristics a finite difference scheme, known in mathematic circles as the modified Richtmyer scheme, is applied to the time domain solution of Maxwell's equations. Both methods should be useful for efficient full wave analysis of three dimensional electromagnetic field problems.
Author: Neven Orhanović
Publisher:
ISBN:
Category : Maxwell equations
Languages : en
Pages : 180
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Book Description
A numerical method based on the the method of characteristics for hyperbolic systems of partial differential equations in four independent variables is developed and used for solving time domain Maxwell's equations. The method uses the characteristic hypersurfaces and the characteristic conditions to derive a set of independent equations relating the electric and magnetic field components on these hypersurfaces. A discretization scheme is developed to solve for the unknown field components at each time step. The method retains many of the good features of the original method of characteristics for hyperbolic systems in two independent variables, such as optimal time step, good behavior near data discontinuities and the ability to treat general boundary conditions. The method is exemplified by calculating the time domain response of a few typical planar interconnect structures to Gaussian and unit step excitations. Although the general emphasis is on interconnect problems, the method is applicable to a number of other transient electromagnetic field problems governed by Maxwell's equations. In addition to the method of characteristics a finite difference scheme, known in mathematic circles as the modified Richtmyer scheme, is applied to the time domain solution of Maxwell's equations. Both methods should be useful for efficient full wave analysis of three dimensional electromagnetic field problems.
Author: John Allan Svigelj
Publisher:
ISBN:
Category :
Languages : en
Pages : 306
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Book Description
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.
Author: Hoang Vinh
Publisher:
ISBN:
Category :
Languages : en
Pages : 234
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Book Description
Author: Jiayuan Fang
Publisher:
ISBN:
Category :
Languages : en
Pages : 372
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Book Description
Author: Joonshik Kim
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Abstract: This dissertation is concerned with the development of numerical techniques for solving Maxwell equations in the time-domain. Two of the main challenges to obtain such solution are, first, how to construct explicit (that is, matrix-free) time-updating formulas without relinquishing the advantage of using irregular unstructured meshes in complex geometries, and second, how to best parallelize the algorithm to solve large-scale problems. The finite element time-domain (FETD) and the finite-difference time-Domain (FDTD) are presently the two most popular methods for solving Maxwell equations in the time-domain. FDTD employs a staggered-grid spatial discretization together with leap-frog style time update scheme to produce a method with many desirable properties such as: conservation of charge and energy, absence of spurious mode, and a simple easy-to-code algorithm. Nevertheless, FDTD (in its conventional form) relies on orthogonal grids, which is a disadvantage when modeling complex geometries. On the other hand, FETD is based upon unstructured grids and hence naturally tailored to handle complex geometries. However, in time-domain simulation (as opposed to frequency-domain simulations), FETD requires a matrix solver at every time step. Since the total number of time steps to produce the overall time-domain solution can be quite large, this requirement demands excessive computational resources. To overcome this problem, we develop a FETD algorithm with "FDTD-like" explicit characteristics. Usually, the system matrices generated after discretizing Maxwell equations in irregular grids are very large and sparse matrices, while their inverses are very large and dense matrices. To construct an explicit algorithm, ideally one would need to somehow obtain and use such inverses. However, these dense matrices are of course not useful in a update scheme because they are not only very costly to compute but also very costly to store for most practical problems. For this reason, we investigate the use of approximate sparse inverses to build update schemes for FETD. We show that the most direct choice, which is to use the approximate inverse of the system matrix itself, is not really an adequate choice because of the nature of the corresponding (continuum) operator, with long-range interactions. We therefore consider instead the use of the approximate inverse of the Hodge (or mass) matrix, which a symmetric positive definite matrix representing a strictly local operator in the continuum limit whose inverse is also local, to compute explicit update schemes. This entails the discretization of Maxwell's equations based on discrete differential forms and the use of a "mixed" set of basis functions for the FETD: Whitney one forms for the electric field intensity and Whitney two forms for the magnetic flux density. This choice of basis functions obeys a discrete version of the de Rham diagram and leads to solutions that are free of spurious modes and numerically stable. We construct a parallel approach to compute the approximate inverse, and provide an error analysis of the resulting solutions versus the density of the approximate inverse and the mesh refinement considered. A higher-order version of the mixed FETD algorithm is also constructed, showing good convergence versus the polynomial order.
Author: Peter Russer
Publisher: Springer Science & Business Media
ISBN: 3540687688
Category : Technology & Engineering
Languages : en
Pages : 423
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Book Description
This book consists of contributions given in honor of Wolfgang J.R. Hoefer. Space and time discretizing time domain methods for electromagnetic full-wave simulation have emerged as key numerical methods in computational electromagnetics. Time domain methods are versatile and can be applied to the solution of a wide range of electromagnetic field problems. Computing the response of an electromagnetic structure to an impulsive excitation localized in space and time provides a comprehensive characterization of the electromagnetic properties of the structure in a wide frequency range. The most important methods are the Finite Difference Time Domain (FDTD) and the Transmission Line Matrix (TLM) methods. The contributions represent the state of the art in dealing with time domain methods in modern engineering electrodynamics for electromagnetic modeling in general, the Transmission Line Matrix (TLM) method, the application of network concepts to electromagnetic field modeling, circuit and system applications and, finally, with broadband devices, systems and measurement techniques.
Author: Atef Z. Elsherbeni
Publisher: IET
ISBN: 1613531753
Category : Computers
Languages : en
Pages : 559
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Book Description
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].
Author: Giovanni Miano
Publisher: Elsevier
ISBN: 0080519598
Category : Technology & Engineering
Languages : en
Pages : 503
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Book Description
The theory of transmission lines is a classical topic of electrical engineering. Recently this topic has received renewed attention and has been a focus of considerable research. This is because the transmisson line theory has found new and important applications in the area of high-speed VLSI interconnects, while it has retained its significance in the area of power transmission. In many applications, transmission lines are connected to nonlinear circuits. For instance, interconnects of high-speed VLSI chips can be modelled as transmission lines loaded with nonlinear elements. These nonlinearities may lead to many new effects such as instability, chaos, generation of higher order harmonics, etc. The mathematical models of transmission lines with nonlinear loads consist of the linear partial differential equations describing the current and voltage dynamics along the lines together with the nonlinear boundary conditions imposed by the nonlinear loads connected to the lines. These nonlinear boundary conditions make the mathematical treatment very difficult. For this reason, the analysis of transmission lines with nonlinear loads has not been addressed adequately in the existing literature. The unique and distinct feature of the proposed book is that it will present systematic, comprehensive, and in-depth analysis of transmission lines with nonlinear loads. - A unified approach for the analysis of networks composed of distributed and lumped circuits - A simple, concise and completely general way to present the wave propagation on transmission lines, including a thorough study of the line equations in characteristic form - Frequency and time domain multiport representations of any linear transmission line - A detailed analysis of the influence on the line characterization of the frequency and space dependence of the line parameters - A rigorous study of the properties of the analytical and numerical solutions of the network equations - The associated discrete circuits and the associated resisitive circuits of transmission lines - Periodic solutions, bifurcations and chaos in transmission lines connected to noninear lumped circuits
Author: Stephen D. Gedney
Publisher: Morgan & Claypool Publishers
ISBN: 160845522X
Category : Computers
Languages : en
Pages : 251
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Book Description
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. 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.
Author: Jian-Ming Jin
Publisher: John Wiley & Sons
ISBN: 1118842022
Category : Science
Languages : en
Pages : 728
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Book Description
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The Finite Element Method in Electromagnetics, Third Edition explains the method’s processes and techniques in careful, meticulous prose and covers not only essential finite element method theory, but also its latest developments and applications—giving engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems. Featuring over thirty percent new material, the third edition of this essential and comprehensive text now includes: A wider range of applications, including antennas, phased arrays, electric machines, high-frequency circuits, and crystal photonics The finite element analysis of wave propagation, scattering, and radiation in periodic structures The time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomena Novel domain decomposition techniques for parallel computation and efficient simulation of large-scale problems, such as phased-array antennas and photonic crystals Along with a great many examples, The Finite Element Method in Electromagnetics is an ideal book for engineering students as well as for professionals in the field.
