Parallel Finite-Difference Time-Domain Method

This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffus

"Written in a manner that is easily digestible to beginners and useful to seasoned professionals, this book introduces the key concepts of computational Finite Difference Time Domain (FDTD) method use

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

The purpose of this book is to provide an up-to-date introduction to the time-domain finite element methods for Maxwell’s equations involving metamaterials. Since the first successful construction of

The common belief is that light is completely reflected by metals. In reality they also exhibit an amazing property that is not so widely known: under some conditions light flows along a metallic surf

This book/CD-ROM graduate-level text presents fundamental techniques of the finite-difference time-domain (FDTD) method as applied to engineering electromagnetics, taking readers from conceptual under

The finite difference time domain (FDTD) method is a common method used in computational electromagnetics that, by its very nature, lends itself to efficient parallel processing. The authors (of the D

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-dom

In this comprehensive reference, Taflove (Northwestern U.), Hagness (U. of Wisconsin-Madison) and contributors explain this critical method for solving Maxwell equations, including the one-dimensional

This book presents and develops new reinforcement learning methods that enable fast and robust learning on robots in real-time.Robots have the potential to solve many problems in society, because of t

Understanding and analysing the complex phenomena related to elastic wave propagation has been the subject of intense research for many years and has enabled application in numerous fields of technolo

Chunyan Li is a course instructor with many years of experience in teaching about time series analysis. His book is essential for students and researchers in oceanography and other subjects in the Earth sciences, looking for a complete coverage of the theory and practice of time series data analysis using MATLAB. This textbook covers the topic's core theory in depth, and provides numerous instructional examples, many drawn directly from the author's own teaching experience, using data files, examples, and exercises. The book explores many concepts, including time; distance on Earth; wind, current, and wave data formats; finding a subset of ship-based data along planned or random transects; error propagation; Taylor series expansion for error estimates; the least squares method; base functions and linear independence of base functions; tidal harmonic analysis; Fourier series and the generalized Fourier transform; filtering techniques: sampling theorems: finite sampling effects; wavelet

Constraint Satisfaction Problems (CSPs) are natural computational problems that appear in many areas of theoretical computer science. Exploring which CSPs are solvable in polynomial time and which are NP-hard reveals a surprising link with central questions in universal algebra. This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs. It includes the required background from logic and combinatorics, particularly model theory and Ramsey theory, and explains the recently discovered link between Ramsey theory and topological dynamics and its implications for CSPs. The book will be of interest to graduate students and researchers in theoretical computer science and to mathematicians in logic, combinatorics, and dynamics who wish to learn about the applications of their work in complexity theory.

In this volume, Mordechai Z. Cohen explores the interpretive methods of Rashi of Troyes (1040–1105), the most influential Jewish Bible commentator of all time. By elucidating the 'plain sense' (peshat) of Scripture, together with critically selected midrashic interpretations, Rashi created an approach that was revolutionary in the talmudically-oriented Ashkenazic milieu. Cohen contextualizes Rashi's commentaries by examining influences from other centers of Jewish learning in Muslim Spain and Byzantine lands. He also opens new scholarly paths by comparing Rashi's methods with trends in Latin learning reflected in the Psalms commentary of his older contemporary, Saint Bruno the Carthusian (1030–1101). Drawing upon the Latin tradition of enarratio poetarum ('interpreting the poets'), Bruno applied a grammatical interpretive method and incorporated patristic commentary selectively, a parallel that Cohen uses to illuminate Rashi's exegetical values. Cohen thereby brings to light the novel

Presenting a fresh look at process control, this new text demonstrates state-space approach shown in parallel with the traditional approach to explain the strategies used in industry today. Modern time-domain and traditional transform-domain methods are integrated throughout and explain the advantages and limitations of each approach; the fundamental theoretical concepts and methods of process control are applied to practical problems. To ensure understanding of the mathematical calculations involved, MATLAB® is included for numeric calculations and MAPLE for symbolic calculations, with the math behind every method carefully explained so that students develop a clear understanding of how and why the software tools work. Written for a one-semester course with optional advanced-level material, features include solved examples, cases that include a number of chemical reactor examples, chapter summaries, key terms, and concepts, as well as over 240 end-of-chapter problems, focused computat

Every fluid dynamicist will at some point need to use computation. Thinking about the physics, constraints and the requirements early on will be rewarded with benefits in time, effort, accuracy and expense. How these benefits can be realised is illustrated in this guide for would-be researchers and beginning graduate students to some of the standard methods and common pitfalls of computational fluid mechanics. Based on a lecture course that the author has developed over twenty years, the text is split into three parts. The quick introduction enables students to solve numerically a basic nonlinear problem by a simple method in just three hours. The follow-up part expands on all the key essentials, including discretisation (finite differences, finite elements and spectral methods), time-stepping and linear algebra. The final part is a selection of optional advanced topics, including hyperbolic equations, the representation of surfaces, the boundary integral method, the multigrid method,

The book reflects the improvements made to the standard algorithm for the finite-difference time-domain (FDTD) method and treatment of absorbing boundary conditions in FDTD, finite element, and transm

Unlike most finite element books that cover time dependent processes (IVPs) in a cursory manner, The Finite Element Method for Initial Value Problems: Mathematics and Computations focuses on the mathe

This monograph presents methods for time domain wave propagation problems. It also describes how to implement them in physical models. Highlights include the construction of 3D finite elements on non

Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and re

This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed i

Advanced Computational Vibroacoustics presents an advanced computational method for the prediction of sound and structural vibrations, in low- and medium-frequency ranges - complex structural acoustics and fluid-structure interaction systems encountered in aerospace, automotive, railway, naval, and energy-production industries. The formulations are presented within a unified computational strategy and are adapted for the present and future generation of massively parallel computers. A reduced-order computational model is constructed using the finite element method for the damped structure and the dissipative internal acoustic fluid (gas or liquid with or without free surface) and using an appropriate symmetric boundary-element method for the external acoustic fluid (gas or liquid). This book allows direct access to computational methods that have been adapted for the future evolution of general commercial software. Written for the global market, it is an invaluable resource for academi

Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate st

This book introduces a general hardware acceleration technique that can significantly speed up finite difference time domain (FDTD) simulations and their applications to engineering problems without r

A unique and comprehensive graduate text and reference on numerical methods for electromagnetic phenomena, from atomistic to continuum scales, in biology, optical-to-micro waves, photonics, nanoelectronics and plasmas. The state-of-the-art numerical methods described include: • Statistical fluctuation formulae for the dielectric constant • Particle-Mesh-Ewald, Fast-Multipole-Method and image-based reaction field method for long-range interactions • High-order singular/hypersingular (Nyström collocation/Galerkin) boundary and volume integral methods in layered media for Poisson–Boltzmann electrostatics, electromagnetic wave scattering and electron density waves in quantum dots • Absorbing and UPML boundary conditions • High-order hierarchical Nédélec edge elements • High-order discontinuous Galerkin (DG) and Yee finite difference time-domain methods • Finite element and plane wave frequency-domain methods for periodic structures • Generalized DG beam propagation method for optic

A comprehensive manual on the efficient modeling and analysis of photonic devices through building numerical codes, this book provides graduate students and researchers with the theoretical background and MATLAB programs necessary for them to start their own numerical experiments. Beginning by summarizing topics in optics and electromagnetism, the book discusses optical planar waveguides, linear optical fiber, the propagation of linear pulses, laser diodes, optical amplifiers, optical receivers, finite-difference time-domain method, beam propagation method and some wavelength division devices, solitons, solar cells and metamaterials. Assuming only a basic knowledge of physics and numerical methods, the book is ideal for engineers, physicists and practising scientists. It concentrates on the operating principles of optical devices, as well as the models and numerical methods used to describe them.

Fundamental principles treated in detail with explanations．Detailed development of array antennas to learn influence of antenna parameters on radiation as well as understanding arrays as used in practice．Thorough survey of antenna types: electrically small, resonant, broadband, and aperture．Emphasis on design data for the antennas treated．Explanations of how antennas are used in systems, such as wireless communications．Many new topics: Low-profile and personal communication antennas, mobile and base station antennas, RFID antennas, dielectric resonator antennas, smart antennas, near fields of antennas, and biohazards of RF exposure．Expanded coverage on: array antennas, microstrip antennas, system applications of antennas, and antenna measurements．Antenna synthesis is covered．Antenna measurement techniques are introduced．This edition includes recent antenna innovations and applications and introduces a succinct treatment of the finite difference, time domain (FDTD) computational techniq

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.

This book presents a theoretical treatment of nonlinear behaviour of solids and structures in such a way that it is suitable for numerical computation, typically using the Finite Element Method. Starting out from elementary concepts, the author systematically uses the principle of virtual work, initially illustrated by truss structures, to give a self-contained and rigorous account of the basic methods. The author illustrates the combination of translations and rotations by finite deformation beam theories in absolute and co-rotation format, and describes the deformation of a three-dimensional continuum in material form. A concise introduction to finite elasticity is followed by an extension to elasto-plastic materials via internal variables and the maximum dissipation principle. Finally, the author presents numerical techniques for solution of the nonlinear global equations and summarises recent results on momentum and energy conserving integration of time-dependent problems. Exercise

This publication provides a comprehensive and systematically organized coverage of higher order finite-difference time-domain or FDTD schemes, demonstrating their potential role as a powerful modeling

This book presents and analyses vortex methods as a tool for the direct numerical simulation of incompressible viscous flows. Vortex methods have matured, offering an interesting alternative to finite difference and spectral methods for high-resolution numerical solutions of the Navier–Stokes equations. Research in the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character that was the motivation for their introduction. Scientists working in the areas of numerical analysis and fluid mechanics will benefit from this book, which may serve both communities as both a reference monograph and a textbook for computational fluid dynamics courses.

The boundary element method is more appropriate than the finite element method to tackle linear, wave propagation, infinite domain, mobile boundaries and unknown boundaries problems. In some engineeri

The focus of this book is the study of the noncommutative aspects of rings and modules, and the style will make it accessible to anyone with a background in basic abstract algebra. Features of interest include an early introduction of projective and injective modules; a module theoretic approach to the Jacobson radical and the Artin-Wedderburn theorem; the use of Baer's criterion for injectivity to prove the structure theorem for finitely generated modules over a principal ideal domain; and applications of the general theory to the representation theory of finite groups. Optional material includes a section on modules over the Weyl algebras and a section on Goldie's theorem. When compared to other more encyclopedic texts, the sharp focus of this book accommodates students meeting this material for the first time. It can be used as a first-year graduate text or as a reference for advanced undergraduates.