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Fast Multipole Boundary Element Method
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Book Synopsis Fast Multipole Boundary Element Method by : Yijun Liu
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.
Book Synopsis Brain and Human Body Modeling 2020 by : Sergey N. Makarov
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.
Book Synopsis Fast Multipole Methods for the Helmholtz Equation in Three Dimensions by : Nail A Gumerov
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
Book Synopsis A Fast Multipole Boundary Element Method and Its Application in Diffusion Problems by : Bo Wang
Download or read book A Fast Multipole Boundary Element Method and Its Application in Diffusion Problems written by Bo Wang and published by . This book was released on 2012 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Element Acoustics written by and published by . This book was released on 2000 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Adaptive Fast Multipole Boundary Element Methods for Three-dimensional Potential and Acoustic Wave Problems by : Liang Shen
Download or read book Adaptive Fast Multipole Boundary Element Methods for Three-dimensional Potential and Acoustic Wave Problems written by Liang Shen and published by . This book was released on 2007 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a numerical method used in the simulations of many potential and acoustic problems, the boundary element method (BEM) has suffered from high solution cost for quite some time, although it has the advantage in the modeling or meshing stage. One way to improve the solution efficiency of the BEM is to use the fast multipole method (FMM). The reduction of the computing cost with the FMM is achieved by using multilevel clustering of the boundary elements, the use of multipole expansions of the fundamental solutions and adaptive fast multipole algorithms. In combination with iterative solvers, the fast multipole boundary element method (FMBEM) is capable of solving many large-scale 3-D problems on desktop PCs. In this dissertation, 3-D adaptive fast multipole boundary element methods for solving large-scale potential (e.g., thermal and electrostatic) and acoustic wave problems are developed. For large-scale potential problems, an adaptive fast multipole algorithm is developed in the FMBEM implementation. The conventional boundary integral equation (CBIE), hyper-singular boundary integral equation (HBIE) and their combination, dual boundary integral equation (CHBIE), are adopted and can be selectively chosen to solve different models. Both the conventional and the new fast multipole method with diagonal translations are implemented and their performances are compared. Implementation issues related to reusing the pre-conditioner and storing the coefficients to further improve the efficiency are addressed. Numerical examples, ranging from simple block models to heat sink and large-scale models of micro-electro-mechanical-systems are tested and presented. For large-scale acoustic problems, a modified version of adaptive fast multipole algorithm is developed for full-space problems first. The Burton-Miller formulation using a linear combination of the CBIE and HBIE is used to overcome the non-uniqueness difficulties in the BIEs for exterior problems. Several large-scale radiation and scattering problems, including scattering and radiating spheres and an engine model are tested. Then, the full-space algorithm is further modified and extended to solving half-space problems. Instead of using a tree structure that contains both real domain and its mirror image, the same tree structure that has been used in the full-space domain is used in the half-pace domain, which greatly simplifies the implementation of half-space FMBEM and reduces the memory storage size. Several examples including spheres sitting on the ground and sound barriers are tested. All the numerical examples of the potential and acoustic problems presented in this dissertation clearly demonstrate the effectiveness and efficiency of the developed adaptive fast multipole boundary element methods. The adaptive FMBEM code for potential problems and the adaptive FMEBM code for acoustic problems have been integrated in a single software package, which is well structured, modularized and extendable to handling other types of problems. Three journal papers have been published based on the work reported in this dissertation, and one journal paper on the half-space problem is in preparation. This dissertation research has significantly advanced the FMBEM for solving large-scale 3-D potential and acoustic problems. The developed adaptive fast multipole algorithms can be easily extended to the FMBEM for 3-D single-domain elasticity, Stokes flow, and multi-domain potential, acoustic, elasticity and Stokes problems for applications in large-scale modeling of composites, functionally-graded materials, micro-electro-mechanical-systems, and biological materials and fluids.
Book Synopsis Fast Multipole Boundary Element Method by : Yijun Liu
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: First book on the fast multipole BEM, bringing together classical theory in BEM formulations and the fast multipole method.
Book Synopsis Recent Advances in Boundary Element Methods by : George Manolis
Download or read book Recent Advances in Boundary Element Methods written by George Manolis and published by Springer Science & Business Media. This book was released on 2009-05-12 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Fast Multipole Boundary Element Method and Its Application to Structure-acoustic Field Interaction by : Matthias Fischer
Download or read book The Fast Multipole Boundary Element Method and Its Application to Structure-acoustic Field Interaction written by Matthias Fischer and published by . This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Boundary Element Method in Acoustics by : Stephen Kirkup
Download or read book The Boundary Element Method in Acoustics written by Stephen Kirkup and published by Stephen Kirkup. This book was released on 1998 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Periodic Boundary Conditions and the Error-controlled Fast Multipole Method by : Ivo Kabadshow
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:
Book Synopsis Fast Boundary Element Methods in Engineering and Industrial Applications by : Ulrich Langer
Download or read book Fast Boundary Element Methods in Engineering and Industrial Applications written by Ulrich Langer and published by Springer Science & Business Media. This book was released on 2012-02-02 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains eight state of the art contributions on mathematical aspects and applications of fast boundary element methods in engineering and industry. This covers the analysis and numerics of boundary integral equations by using differential forms, preconditioning of hp boundary element methods, the application of fast boundary element methods for solving challenging problems in magnetostatics, the simulation of micro electro mechanical systems, and for contact problems in solid mechanics. Other contributions are on recent results on boundary element methods for the solution of transient problems. This book is addressed to researchers, graduate students and practitioners working on and using boundary element methods. All contributions also show the great achievements of interdisciplinary research between mathematicians and engineers, with direct applications in engineering and industry.
Book Synopsis The Multilevel Fast Multipole Algorithm (MLFMA) for Solving Large-Scale Computational Electromagnetics Problems by : Ozgur Ergul
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.
Book Synopsis Implementation of the Fast Multipole Boundary Element Method (FMBEM) for Sound Field Calculations by : Sune Grau Ellegaard
Download or read book Implementation of the Fast Multipole Boundary Element Method (FMBEM) for Sound Field Calculations written by Sune Grau Ellegaard and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fast Multipole Boundary Element Method for Solving Two-dimensional Acoustic Wave Problems by : Milind Shrikant Bapat
Download or read book Fast Multipole Boundary Element Method for Solving Two-dimensional Acoustic Wave Problems written by Milind Shrikant Bapat and published by . This book was released on 2006 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: The boundary element method (BEM) is a numerical method for solving boundary value problems. The boundary element method has a clear advantage over other techniques like finite element method (FEM) in problems involving infinite domains. Hence the boundary element method has found many applications in the field of acoustics which often exist in infinite domains. The traditional approach for finding solutions to acoustic problems using the boundary element method has a computational complexity of the order O(N 2). This makes the computation very slow as the number of nodes increase. A new technique called fast multipole method (FMM) has emerged in the last decade. Replacing the normal matrix-vector multiplication with the fast multipole method reduces the computational time to order O(N). In this thesis the fast multipole method has been used to accelerate the boundary element method for 2-D acoustic wave problems. The relevant formulae are derived. It is shown that the computational time is of the order O(N) for this formulation. It is also observed that the memory required is much lesser and hence larger models can be solved. The formulation is a very basic one and gives good results as shown by the numerical examples. Use of higher-order elements and hypersingular formulation will result in a very capable and robust solver in the future.
Book Synopsis Introduction to the Fast Multipole Method by : Victor Anisimov
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
Book Synopsis The Finite Element Method in Electromagnetics by : Jian-Ming Jin
Download or read book The Finite Element Method in Electromagnetics written by Jian-Ming Jin and published by John Wiley & Sons. This book was released on 2015-02-18 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The Finite Element Method in Electromagnetics, Third Edition explains the method’s processes and techniques in careful, meticulous prose and covers not only essential finite element method theory, but also its latest developments and applications—giving engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems. Featuring over thirty percent new material, the third edition of this essential and comprehensive text now includes: A wider range of applications, including antennas, phased arrays, electric machines, high-frequency circuits, and crystal photonics The finite element analysis of wave propagation, scattering, and radiation in periodic structures The time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomena Novel domain decomposition techniques for parallel computation and efficient simulation of large-scale problems, such as phased-array antennas and photonic crystals Along with a great many examples, The Finite Element Method in Electromagnetics is an ideal book for engineering students as well as for professionals in the field.
