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

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.

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.

During the existence of the project, we designed Fast Multipole algorithms for the solution of the Laplace and Helmholtz equations, the latter predominately in the low-frequency regime. The principal analytical apparatus used were the new diagonal forms of translation operators for the Laplace and Helmholtz equation; such diagonal forms in turn required the use of Generalized Gaussian Quadratures, which we have also designed. In addition, we redesigned the logical structure of such algorithms, drastically reducing their memory requirements. At the present time, extremely efficient Fast Multipole Methods for the Laplace equation in three dimensions are in existence; the construction of such schemes for the Helmholtz equation in the low-frequency regime has been reduced to a purely programming task. Six publications reporting this work have appeared (or been accepted) in refereed journals; two publications have been released in the report form, and are about to be submitted to refereed journals; three publications are in preparation.

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.

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.

First book on the fast multipole BEM, bringing together classical theory in BEM formulations and the fast multipole method.