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Adaptive Mesh Refinement for Time-domain Numerical Electromagnetics

Author: Costas D. Sarris

Publisher: Morgan & Claypool Publishers

Published: 2007

Total Pages: 154

ISBN-13: 1598290789

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

Published: 2022-05-31

Total Pages: 135

ISBN-13: 3031016955

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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

Published: 2011-04-07

Total Pages: 405

ISBN-13: 1139497987

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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.

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

Author: Stephen Gedney

Publisher: Springer Nature

Published: 2022-05-31

Total Pages: 242

ISBN-13: 3031017129

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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

Published: 2022-06-01

Total Pages: 122

ISBN-13: 3031017137

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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

Adaptive Mesh Refinement for Pseudospectral Methods in Numerical Relativity

Author: Sarah Renkhoff

Publisher:

Published: 2023*

Total Pages: 0

ISBN-13:

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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.

MRTD (Multi Resolution Time Domain) Method in Electromagnetics

Author: Nathan Bushyager

Publisher: Morgan & Claypool Publishers

Published: 2006-12-01

Total Pages: 116

ISBN-13: 1598290150

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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.

Boundary Elements and Other Mesh Reduction Methods Twenty-eight

Author: C. A. Brebbia

Publisher: WIT Press

Published: 2006

Total Pages: 361

ISBN-13: 1845641647

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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

Published: 1998

Total Pages: 766

ISBN-13:

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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.

Time Domain Techniques in Computational Electromagnetics

Author: Dragan Poljak

Publisher: Witpress

Published: 2004

Total Pages: 192

ISBN-13:

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A state-of-the-art review from invited contributors. Subjects covered include: time domain analysis of electromagnetic wave fields by boundary; integral equation method; and transient analysis of thin wires and related time domain energy measures.