Fast Multipole Methods for the Helmholtz Equation in Three Dimensions
Fast Multipole Methods for the Helmholtz Equation in Three Dimensions

Author: Nail A Gumerov

Publisher: Elsevier

Published: 2005-01-27

Total Pages: 551

ISBN-13: 0080531598

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This volume in the Elsevier Series in Electromagnetism presents a detailed, in-depth and self-contained treatment of the Fast Multipole Method and its applications to the solution of the Helmholtz equation in three dimensions. The Fast Multipole Method was pioneered by Rokhlin and Greengard in 1987 and has enjoyed a dramatic development and recognition during the past two decades. This method has been described as one of the best 10 algorithms of the 20th century. Thus, it is becoming increasingly important to give a detailed exposition of the Fast Multipole Method that will be accessible to a broad audience of researchers. This is exactly what the authors of this book have accomplished. For this reason, it will be a valuable reference for a broad audience of engineers, physicists and applied mathematicians. - The Only book that provides comprehensive coverage of this topic in one location - Presents a review of the basic theory of expansions of the Helmholtz equation solutions - Comprehensive description of both mathematical and practical aspects of the fast multipole method and it's applications to issues described by the Helmholtz equation

Fast Multipole Boundary Element Method
Fast Multipole Boundary Element Method

Author: Yijun Liu

Publisher: Cambridge University Press

Published: 2009-08-24

Total Pages: 255

ISBN-13: 113947944X

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The fast multipole method is one of the most important algorithms in computing developed in the 20th century. Along with the fast multipole method, the boundary element method (BEM) has also emerged as a powerful method for modeling large-scale problems. BEM models with millions of unknowns on the boundary can now be solved on desktop computers using the fast multipole BEM. This is the first book on the fast multipole BEM, which brings together the classical theories in BEM formulations and the recent development of the fast multipole method. Two- and three-dimensional potential, elastostatic, Stokes flow, and acoustic wave problems are covered, supplemented with exercise problems and computer source codes. Applications in modeling nanocomposite materials, bio-materials, fuel cells, acoustic waves, and image-based simulations are demonstrated to show the potential of the fast multipole BEM. Enables students, researchers, and engineers to learn the BEM and fast multipole method from a single source.

Computational Simulation in Architectural and Environmental Acoustics
Computational Simulation in Architectural and Environmental Acoustics

Author: Tetsuya Sakuma

Publisher: Springer

Published: 2014-08-05

Total Pages: 332

ISBN-13: 4431544542

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This book reviews a variety of methods for wave-based acoustic simulation and recent applications to architectural and environmental acoustic problems. Following an introduction providing an overview of computational simulation of sound environment, the book is in two parts: four chapters on methods and four chapters on applications. The first part explains the fundamentals and advanced techniques for three popular methods, namely, the finite-difference time-domain method, the finite element method, and the boundary element method, as well as alternative time-domain methods. The second part demonstrates various applications to room acoustics simulation, noise propagation simulation, acoustic property simulation for building components, and auralization. This book is a valuable reference that covers the state of the art in computational simulation for architectural and environmental acoustics.

Excursions in Harmonic Analysis, Volume 3
Excursions in Harmonic Analysis, Volume 3

Author: Radu Balan

Publisher: Birkhäuser

Published: 2015-06-02

Total Pages: 344

ISBN-13: 331913230X

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This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 – 2013. Containing cutting-edge results by an impressive array of mathematicians, engineers, and scientists in academia, industry, and government, it will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, physics, and engineering. Topics covered include · spectral analysis and correlation; · radar and communications: design, theory, and applications; · sparsity · special topics in harmonic analysis. The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.

Recent Advances in Boundary Element Methods
Recent Advances in Boundary Element Methods

Author: George Manolis

Publisher: Springer Science & Business Media

Published: 2009-05-12

Total Pages: 467

ISBN-13: 1402097107

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This volume, dedicated to Professor Dimitri Beskos, contains contributions from leading researchers in Europe, the USA, Japan and elsewhere, and addresses the needs of the computational mechanics research community in terms of timely information on boundary integral equation-based methods and techniques applied to a variety of fields. The contributors are well-known scientists, who also happen to be friends, collaborators as past students of Dimitri Beskos. Dimitri is one the BEM pioneers who started his career at the University of Minnesota in Minneapolis, USA, in the 1970s and is now with the University of Patras in Patras, Greece. The book is essentially a collection of both original and review articles on contemporary Boundary Element Methods (BEM) as well as on the newer Mesh Reduction Methods (MRM), covering a variety of research topics. Close to forty contributions compose an over-500 page volume that is rich in detail and wide in terms of breadth of coverage of the subject of integral equation formulations and solutions in both solid and fluid mechanics.

Fast Multipole Boundary Element Method
Fast Multipole Boundary Element Method

Author: Yijun Liu

Publisher: Cambridge University Press

Published: 2009-08-24

Total Pages: 255

ISBN-13: 0521116597

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First book on the fast multipole BEM, bringing together classical theory in BEM formulations and the fast multipole method.

Radial Basis Function Methods For Large-Scale Wave Propagation
Radial Basis Function Methods For Large-Scale Wave Propagation

Author: Jun-Pu Li

Publisher: Bentham Science Publishers

Published: 2021-12-24

Total Pages: 183

ISBN-13: 1681088991

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This book details the development of techniques and ideas from the radial basis function. It begins with a mathematical description of the basic concept of radial function method with chapters progressively delving into the derivation and construction of radial basis functions for large-scale wave propagation problems including singularity problems, high-frequency wave problems and large-scale computation problems. This reference, written by experts in numerical analysis, demonstrates how the functions arise naturally in mathematical analyses of structures responding to external loads. Readers are also equipped with mathematical knowledge about the radial basis function for understanding key algorithms required for practical solutions. Key features: - Introduces basic concepts of radial basis function methods - Provides detailed derivations of several radial basis functions - Explains complex problems using simple language - Contains a wide range of numerical examples to demonstrate applications of relevant functions - Combines the radial basis function with other known numerical methods (boundary element methods and differential equations). - Includes references and appropriate chapter appendices - Includes MATLAB codes for origin intensity factors and nearly singular factors for radial basis calculations The book is designed to make information about radial basis function methods more accessible to research scientists, professional engineers and postgraduate students, with a specific focus on large-scale wave propagation problems.

GPU Computing Gems Emerald Edition
GPU Computing Gems Emerald Edition

Author:

Publisher: Elsevier

Published: 2011-01-13

Total Pages: 889

ISBN-13: 0123849896

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GPU Computing Gems Emerald Edition offers practical techniques in parallel computing using graphics processing units (GPUs) to enhance scientific research. The first volume in Morgan Kaufmann's Applications of GPU Computing Series, this book offers the latest insights and research in computer vision, electronic design automation, and emerging data-intensive applications. It also covers life sciences, medical imaging, ray tracing and rendering, scientific simulation, signal and audio processing, statistical modeling, video and image processing. This book is intended to help those who are facing the challenge of programming systems to effectively use GPUs to achieve efficiency and performance goals. It offers developers a window into diverse application areas, and the opportunity to gain insights from others' algorithm work that they may apply to their own projects. Readers will learn from the leading researchers in parallel programming, who have gathered their solutions and experience in one volume under the guidance of expert area editors. Each chapter is written to be accessible to researchers from other domains, allowing knowledge to cross-pollinate across the GPU spectrum. Many examples leverage NVIDIA's CUDA parallel computing architecture, the most widely-adopted massively parallel programming solution. The insights and ideas as well as practical hands-on skills in the book can be immediately put to use. Computer programmers, software engineers, hardware engineers, and computer science students will find this volume a helpful resource. For useful source codes discussed throughout the book, the editors invite readers to the following website: ..." - Covers the breadth of industry from scientific simulation and electronic design automation to audio / video processing, medical imaging, computer vision, and more - Many examples leverage NVIDIA's CUDA parallel computing architecture, the most widely-adopted massively parallel programming solution - Offers insights and ideas as well as practical "hands-on" skills you can immediately put to use

Theory and Computation of Electromagnetic Fields
Theory and Computation of Electromagnetic Fields

Author: Jian-Ming Jin

Publisher: John Wiley & Sons

Published: 2015-08-26

Total Pages: 756

ISBN-13: 1119108098

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Reviews the fundamental concepts behind the theory and computation of electromagnetic fields The book is divided in two parts. The first part covers both fundamental theories (such as vector analysis, Maxwell’s equations, boundary condition, and transmission line theory) and advanced topics (such as wave transformation, addition theorems, and fields in layered media) in order to benefit students at all levels. The second part of the book covers the major computational methods for numerical analysis of electromagnetic fields for engineering applications. These methods include the three fundamental approaches for numerical analysis of electromagnetic fields: the finite difference method (the finite difference time-domain method in particular), the finite element method, and the integral equation-based moment method. The second part also examines fast algorithms for solving integral equations and hybrid techniques that combine different numerical methods to seek more efficient solutions of complicated electromagnetic problems. Theory and Computation of Electromagnetic Fields, Second Edition: Provides the foundation necessary for graduate students to learn and understand more advanced topics Discusses electromagnetic analysis in rectangular, cylindrical and spherical coordinates Covers computational electromagnetics in both frequency and time domains Includes new and updated homework problems and examples Theory and Computation of Electromagnetic Fields, Second Edition is written for advanced undergraduate and graduate level electrical engineering students. This book can also be used as a reference for professional engineers interested in learning about analysis and computation skills.