Fast Multipole Methods For The Helmholtz Equation In Three Dimensions

Author : Nail A Gumerov
Publisher : Elsevier
ISBN 13 : 0080531598
Total Pages : 551 pages
Book Rating : 4.95/5 ( download)

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Download or read book Fast Multipole Methods for the Helmholtz Equation in Three Dimensions written by Nail A Gumerov and published by Elsevier. This book was released on 2005-01-27 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Yijun Liu
Publisher : Cambridge University Press
ISBN 13 : 113947944X
Total Pages : 255 pages
Book Rating : 4.48/5 ( download)

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Download or read book Fast Multipole Boundary Element Method written by Yijun Liu and published by Cambridge University Press. This book was released on 2009-08-24 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Per-Gunnar Martinsson
Publisher : SIAM
ISBN 13 : 1611976049
Total Pages : 332 pages
Book Rating : 4.45/5 ( download)

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Download or read book Fast Direct Solvers for Elliptic PDEs written by Per-Gunnar Martinsson and published by SIAM. This book was released on 2019-12-16 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.

Author : Ivo Kabadshow
Publisher : Forschungszentrum Jülich
ISBN 13 : 3893367705
Total Pages : 143 pages
Book Rating : 4.02/5 ( download)

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Download or read book Periodic Boundary Conditions and the Error-controlled Fast Multipole Method written by Ivo Kabadshow and published by Forschungszentrum Jülich. This book was released on 2012 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Radu Balan
Publisher : Birkhäuser
ISBN 13 : 331913230X
Total Pages : 336 pages
Book Rating : 4.03/5 ( download)

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Download or read book Excursions in Harmonic Analysis, Volume 3 written by Radu Balan and published by Birkhäuser. This book was released on 2015-06-02 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Bjorn Engquist
Publisher : Cambridge University Press
ISBN 13 : 0521134439
Total Pages : 254 pages
Book Rating : 4.39/5 ( download)

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Download or read book Highly Oscillatory Problems written by Bjorn Engquist and published by Cambridge University Press. This book was released on 2009-07-02 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Review papers from experts in areas of active research into highly oscillatory problems, with an emphasis on computation.

Author : Jun-Pu Li
Publisher : Bentham Science Publishers
ISBN 13 : 1681088991
Total Pages : 183 pages
Book Rating : 4.90/5 ( download)

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Download or read book Radial Basis Function Methods For Large-Scale Wave Propagation written by Jun-Pu Li and published by Bentham Science Publishers. This book was released on 2021-12-24 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jian-Ming Jin
Publisher : John Wiley & Sons
ISBN 13 : 1119108098
Total Pages : 756 pages
Book Rating : 4.92/5 ( download)

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Download or read book Theory and Computation of Electromagnetic Fields written by Jian-Ming Jin and published by John Wiley & Sons. This book was released on 2015-08-26 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author :
Publisher : Elsevier
ISBN 13 : 9780123849892
Total Pages : 886 pages
Book Rating : 4.96/5 ( download)

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Download or read book GPU Computing Gems Emerald Edition written by and published by Elsevier. This book was released on 2011-01-13 with total page 886 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : A.H-D. Cheng
Publisher : WIT Press
ISBN 13 : 1784660272
Total Pages : 361 pages
Book Rating : 4.77/5 ( download)

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Download or read book Boundary Elements and Other Mesh Reduction Methods XXXVIII written by A.H-D. Cheng and published by WIT Press. This book was released on 2015-11-16 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing the latest in a long line of conferences covering the most recent advances in Boundary Elements and Mesh Reduction Methods (BEM/MRM), this book contains an important chapter in the history of this important method used in science and engineering. The BEM/MRM conference has long been recognised as THE international forum on the technique. The proceedings of the conference therefore constitute a record of the development of the method, running from the initial successful development of boundary integral techniques into the BEM, a method that eliminates the need for an internal mesh, to the recent and most sophisticated Mesh Reduction and even Meshless Methods. Since the boundary elements, mesh reduction, and meshless methods are used in many engineering and scientific fields, the book will be of great interest to all engineers and scientists working within the areas of numerical analysis, boundary elements and meshless methods. Topics covered include: Advanced formulations; Advanced meshless and mesh reduction methods; Structural mechanics applications; Solid mechanics; Heat and mass transfer, Electrical engineering and electromagnetics; Computational methods; Fluid flow modelling; Damage mechanics and fracture; Dynamics and Vibrations Engineering applications.