Implementation of the Fast Multipole Boundary Element Method (FMBEM) for Sound Field Calculations PDF Download
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Author: Sune Grau Ellegaard
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Sune Grau Ellegaard
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Liang Shen
Publisher:
ISBN:
Category :
Languages : en
Pages : 122
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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.
Author: Yijun Liu
Publisher: Cambridge University Press
ISBN: 113947944X
Category : Technology & Engineering
Languages : en
Pages : 255
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Book Description
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: Xavier Vuylsteke
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Described as one of the best ten algorithms of the 20th century, the fast multipole formalism applied to the boundary element method allows to handle large problems which were inconceivable only a few years ago. Thus, the motivation of the present work is to assess the ability, as well as the benefits in term of computational resources provided by the application of this formalism to the boundary element method, for solving sound propagation problems and providing reference solutions, in three dimensional dense urban environments, in the aim of assessing or improving fast engineering tools. We first introduce the mathematical background required for the derivation of the boundary integral equation, for solving sound propagation problems in unbounded domains. We discuss the conventional and hyper-singular boundary integral equation to overcome the numerical artifact of fictitious eigen-frequencies, when solving exterior problems. We then make a brief historical and technical overview of the fast multipole principle and introduce the mathematical tools required to expand the elementary solution of the Helmholtz equation and describe the main steps, from a numerical viewpoint, of fast multipole calculations. A sound propagation problem in a city block made of 5 buildings allows us to highlight instabilities in the recursive computation of translation matrices, resulting in discontinuities of the surface pressure and a no convergence of the iterative solver. This observation leads us to consider the very recent work of Gumerov & Duraiswamy, related to a ``stable'' recursive computation of rotation matrices coefficients in the RCR decomposition. This new improved algorithm has been subsequently assessed successfully on a multi scattering problem up to a dimensionless domain size equal to 207 wavelengths. We finally performed comparisons between a BEM algorithm, extit{Micado3D}, the FMBEM algorithm and a ray tracing algorithm, Icare, for the calculation of averaged pressure levels in an opened and closed court yards. The fast multipole algorithm allowed to validate the results computed with Icare in the opened court yard up to 300 Hz corresponding, (i.e. 100 wavelengths), while in the closed court yard, a very sensitive area without direct or reflective fields, further investigations related to the preconditioning seem required to ensure reliable solutions provided by iterative solver based algorithms.
Author: Bo Wang
Publisher:
ISBN:
Category : Boundary element methods
Languages : en
Pages : 74
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Author: Milind Shrikant Bapat
Publisher:
ISBN:
Category :
Languages : en
Pages : 85
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Book Description
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.
Author: Matthias Fischer
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Nail A Gumerov
Publisher: Elsevier
ISBN: 0080531598
Category : Mathematics
Languages : en
Pages : 551
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Book Description
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: George Manolis
Publisher: Springer Science & Business Media
ISBN: 1402097107
Category : Technology & Engineering
Languages : en
Pages : 467
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Book Description
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.
Author: Tetsuya Sakuma
Publisher: Springer
ISBN: 4431544542
Category : Technology & Engineering
Languages : en
Pages : 332
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Book Description
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.
