Introduction To The Fast Multipole Method

Author : Victor Anisimov
Publisher : CRC Press
ISBN 13 : 1439839069
Total Pages : 459 pages
Book Rating : 4.65/5 ( download)

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Download or read book Introduction to the Fast Multipole Method written by Victor Anisimov and published by CRC Press. This book was released on 2019-12-06 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the Fast Multipole Method introduces the reader to the theory and computer implementation of the Fast Multipole Method. It covers the topics of Laplace’s equation, spherical harmonics, angular momentum, the Wigner matrix, the addition theorem for solid harmonics, and lattice sums for periodic boundary conditions, along with providing a complete, self-contained explanation of the math of the method, so that anyone having an undergraduate grasp of calculus should be able to follow the material presented. The authors derive the Fast Multipole Method from first principles and systematically construct the theory connecting all the parts. Key Features Introduces each topic from first principles Derives every equation presented, and explains each step in its derivation Builds the necessary theory in order to understand, develop, and use the method Describes the conversion from theory to computer implementation Guides through code optimization and parallelization

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 : Victor Anisimov
Publisher : CRC Press
ISBN 13 : 9781439839058
Total Pages : 432 pages
Book Rating : 4.50/5 ( download)

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Download or read book Introduction to Quantum Biology written by Victor Anisimov and published by CRC Press. This book was released on 2016-08-15 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to the theory and methodology of quantum-mechanical modeling of chemical and biological systems. Given the immense complexity of such systems, there is a constant search for new methods. The goal of this text is to derive approximate (semi-empirical) methods to address this class of problems and to provide insight for their continued development. The authors cover such important topics as molecular dynamics, high performance computing, free energy calculations, statistical mechanics, long-range electrostatics, and many-electron systems. They also discuss applications for water salvation, chemical reactions, conformational sampling, and structure relaxation.

Author : Sergey N. Makarov
Publisher : Springer Nature
ISBN 13 : 3030456234
Total Pages : 395 pages
Book Rating : 4.38/5 ( download)

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Download or read book Brain and Human Body Modeling 2020 written by Sergey N. Makarov and published by Springer Nature. This book was released on 2021 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 41st Annual International Conference of the IEEE EMBS, took place between July 23 and 27, 2019, in Berlin, Germany. The focus was on "Biomedical engineering ranging from wellness to intensive care." This conference provided an opportunity for researchers from academia and industry to discuss a variety of topics relevant to EMBS and hosted the 4th Annual Invited Session on Computational Human Models. At this session, a bevy of research related to the development of human phantoms was presented, together with a substantial variety of practical applications explored through simulation.

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 : Susanne Pfalzner
Publisher : Cambridge University Press
ISBN 13 : 9780521019163
Total Pages : 184 pages
Book Rating : 4.68/5 ( download)

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Download or read book Many-Body Tree Methods in Physics written by Susanne Pfalzner and published by Cambridge University Press. This book was released on 2005-09-08 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studying the dynamics of a large number of particles interacting through long-range forces, commonly referred to as the "N-body problem", is a central aspect of many different branches of physics. In recent years, physicists have made significant advances in the development of fast N-body algorithms to deal efficiently with such complex problems. This book gives a thorough introduction to these so-called "tree methods", setting out the basic principles and giving many practical examples of their use. The authors assume no prior specialist knowledge, and they illustrate the techniques throughout with reference to a broad range of applications. The book will be of great interest to graduate students and researchers working on the modeling of systems in astrophysics, plasma physics, nuclear and particle physics, condensed matter physics and materials science.

Author : Ozgur Ergul
Publisher : John Wiley & Sons
ISBN 13 : 1118844912
Total Pages : 484 pages
Book Rating : 4.15/5 ( download)

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Download or read book The Multilevel Fast Multipole Algorithm (MLFMA) for Solving Large-Scale Computational Electromagnetics Problems written by Ozgur Ergul and published by John Wiley & Sons. This book was released on 2014-04-22 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Multilevel Fast Multipole Algorithm (MLFMA) for Solving Large-Scale Computational Electromagnetic Problems provides a detailed and instructional overview of implementing MLFMA. The book: Presents a comprehensive treatment of the MLFMA algorithm, including basic linear algebra concepts, recent developments on the parallel computation, and a number of application examples Covers solutions of electromagnetic problems involving dielectric objects and perfectly-conducting objects Discusses applications including scattering from airborne targets, scattering from red blood cells, radiation from antennas and arrays, metamaterials etc. Is written by authors who have more than 25 years experience on the development and implementation of MLFMA The book will be useful for post-graduate students, researchers, and academics, studying in the areas of computational electromagnetics, numerical analysis, and computer science, and who would like to implement and develop rigorous simulation environments based on MLFMA.

Author : Volodymyr Kushch
Publisher : Butterworth-Heinemann
ISBN 13 : 0124076602
Total Pages : 507 pages
Book Rating : 4.00/5 ( download)

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Download or read book Micromechanics of Composites written by Volodymyr Kushch and published by Butterworth-Heinemann. This book was released on 2013-05-13 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Micromechanics of Composites: Multipole Expansion Approach is the first book to introduce micromechanics researchers to a more efficient and accurate alternative to computational micromechanics, which requires heavy computational effort and the need to extract meaningful data from a multitude of numbers produced by finite element software code. In this book Dr. Kushch demonstrates the development of the multipole expansion method, including recent new results in the theory of special functions and rigorous convergence proof of the obtained series solutions. The complete analytical solutions and accurate numerical data contained in the book have been obtained in a unified manner for a number of the multiple inclusion models of finite, semi- and infinite heterogeneous solids. Contemporary topics of micromechanics covered in the book include composites with imperfect and partially debonded interface, nanocomposites, cracked solids, statistics of the local fields, and brittle strength of disordered composites. Contains detailed analytical and numerical analyses of a variety of micromechanical multiple inclusion models, providing clear insight into the physical nature of the problems under study Provides researchers with a reliable theoretical framework for developing the micromechanical theories of a composite’s strength, brittle/fatigue damage development and other properties Includes a large amount of highly accurate numerical data and plots for a variety of model problems, serving as a benchmark for testing the applicability of existing approximate models and accuracy of numerical solutions

Author : Björn Engquist
Publisher : Springer
ISBN 13 : 9783662528723
Total Pages : 0 pages
Book Rating : 4.2X/5 ( download)

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Download or read book Encyclopedia of Applied and Computational Mathematics written by Björn Engquist and published by Springer. This book was released on 2016-12-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: EACM is a comprehensive reference work covering the vast field of applied and computational mathematics. Applied mathematics itself accounts for at least 60 per cent of mathematics, and the emphasis on computation reflects the current and constantly growing importance of computational methods in all areas of applications. EACM emphasizes the strong links of applied mathematics with major areas of science, such as physics, chemistry, biology, and computer science, as well as specific fields like atmospheric ocean science. In addition, the mathematical input to modern engineering and technology form another core component of EACM.

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.