Fast Multipole Accelerated Boundary Element Methods for Room Acoustics PDF Download
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Author: James F. Lynch
Publisher:
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Category :
Languages : en
Pages :
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Author: James F. Lynch
Publisher:
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Languages : en
Pages :
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Author: Milind Shrikant Bapat
Publisher:
ISBN:
Category :
Languages : en
Pages : 85
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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: Yijun Liu
Publisher: Cambridge University Press
ISBN: 113947944X
Category : Technology & Engineering
Languages : en
Pages : 255
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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.
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: Shuvra S. Bhattacharyya
Publisher: Springer Science & Business Media
ISBN: 1441963456
Category : Technology & Engineering
Languages : en
Pages : 1099
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It gives me immense pleasure to introduce this timely handbook to the research/- velopment communities in the ?eld of signal processing systems (SPS). This is the ?rst of its kind and represents state-of-the-arts coverage of research in this ?eld. The driving force behind information technologies (IT) hinges critically upon the major advances in both component integration and system integration. The major breakthrough for the former is undoubtedly the invention of IC in the 50’s by Jack S. Kilby, the Nobel Prize Laureate in Physics 2000. In an integrated circuit, all components were made of the same semiconductor material. Beginning with the pocket calculator in 1964, there have been many increasingly complex applications followed. In fact, processing gates and memory storage on a chip have since then grown at an exponential rate, following Moore’s Law. (Moore himself admitted that Moore’s Law had turned out to be more accurate, longer lasting and deeper in impact than he ever imagined. ) With greater device integration, various signal processing systems have been realized for many killer IT applications. Further breakthroughs in computer sciences and Internet technologies have also catalyzed large-scale system integration. All these have led to today’s IT revolution which has profound impacts on our lifestyle and overall prospect of humanity. (It is hard to imagine life today without mobiles or Internets!) The success of SPS requires a well-concerted integrated approach from mul- ple disciplines, such as device, design, and application.
Author: Matthias Fischer
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Ulrich Langer
Publisher: Springer Science & Business Media
ISBN: 3642256708
Category : Technology & Engineering
Languages : en
Pages : 278
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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.
Author: Sune Grau Ellegaard
Publisher:
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Category :
Languages : en
Pages :
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Author: Yoiti Suzuki
Publisher: World Scientific
ISBN: 9814465410
Category : Psychology
Languages : en
Pages : 518
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Humans possess a remarkable ability to extract rich three-dimensional information about sound environments simply by analyzing the acoustic signals they receive at their two ears. Research in spatial hearing has evolved from a theoretical discipline studying the basic mechanisms of hearing to a technical discipline focused on designing and implementing increasingly sophisticated spatial auditory display systems. This book contains 39 chapters representing the current state-of-the-art in spatial audio research selected from papers presented in Sendai, Japan, at the First International Workshop on the Principles and Applications of Spatial Hearing.
Author: Alexander K. Belyaev
Publisher: Springer Science & Business Media
ISBN: 9400702892
Category : Technology & Engineering
Languages : en
Pages : 471
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The Symposium was aimed at the theoretical and numerical problems involved in modelling the dynamic response of structures which have uncertain properties due to variability in the manufacturing and assembly process, with automotive and aerospace structures forming prime examples. It is well known that the difficulty in predicting the response statistics of such structures is immense, due to the complexity of the structure, the large number of variables which might be uncertain, and the inevitable lack of data regarding the statistical distribution of these variables. The Symposium participants presented the latest thinking in this very active research area, and novel techniques were presented covering the full frequency spectrum of low, mid, and high frequency vibration problems. It was demonstrated that for high frequency vibrations the response statistics can saturate and become independent of the detailed distribution of the uncertain system parameters. A number of presentations exploited this physical behaviour by using and extending methods originally developed in both phenomenological thermodynamics and in the fields of quantum mechanics and random matrix theory. For low frequency vibrations a number of presentations focussed on parametric uncertainty modelling (for example, probabilistic models, interval analysis, and fuzzy descriptions) and on methods of propagating this uncertainty through a large dynamic model in an effi cient way. At mid frequencies the problem is mixed, and various hybrid schemes were proposed. It is clear that a comprehensive solution to the problem of predicting the vibration response of uncertain structures across the whole frequency range requires expertise across a wide range of areas (including probabilistic and non-probabilistic methods, interval and info-gap analysis, statistical energy analysis, statistical thermodynamics, random wave approaches, and large scale computations) and this IUTAM symposium presented a unique opportunity to bring together outstanding international experts in these fields.
