@article {13975, title = {A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation}, journal = {The Journal of the Acoustical Society of America}, volume = {125}, year = {2009}, month = {2009///}, pages = {191 - 205}, abstract = {The development of a fast multipole method (FMM) accelerated iterative solution of the boundary element method (BEM) for the Helmholtz equations in three dimensions is described. The FMM for the Helmholtz equation is significantly different for problems with low and high kD (where k is the wavenumber and D the domain size), and for large problems the method must be switched between levels of the hierarchy. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements), and these errors must be balanced against approximations introduced by the FMM and the convergence criterion for iterative solution. These different errors must all be chosen in a way that, on the one hand, excess work is not done and, on the other, that the error achieved by the overall computation is acceptable. Details of translation operators for low and high kD, choice of representations, and BEM quadrature schemes, all consistent with these approximations, are described. A novel preconditioner using a low accuracy FMM accelerated solver as a right preconditioner is also described. Results of the developed solvers for large boundary value problems with 0.0001≲kD≲500 are presented and shown to perform close to theoretical expectations.}, keywords = {acoustic wave scattering, boundary-elements methods, boundary-value problems, Helmholtz equations, iterative methods}, doi = {10.1121/1.3021297}, url = {http://link.aip.org/link/?JAS/125/191/1}, author = {Gumerov, Nail A. and Duraiswami, Ramani} } @article {14030, title = {Computation of scattering from clusters of spheres using the fast multipole method}, journal = {The Journal of the Acoustical Society of America}, volume = {117}, year = {2005}, month = {2005///}, pages = {1744 - 1761}, abstract = {A T-matrix based method of solution of the multiple scattering problem was presented by the authors [J. Acoust Soc. Am. 112, 2688{\textendash}2701 (2002)]. This method can be applied to the computation of relatively small problems, since the number of operations required grows with the number of spheres N as O(N3), and with the sixth power of the wave number. The use of iterative techniques accelerated using the fast multipole method (FMM) can accelerate this solution, as presented by Koc and Chew [J. Acoust. Soc. Am. 103, 721{\textendash}734 (1998)] originally. In this study we present a method that combines preconditioned Krylov subspace iterative techniques, FMM accelerated matrix vector products, a novel FMM-based preconditioner, and fast translation techniques that enable us to achieve an overall algorithm in which the cost of the matrix-vector multiplication grows with N as O(N log N) and with the third power of the wave number. We discuss the convergence of the iterative techniques, selection of the truncation number, errors in the solution, and other issues. The results of the solution of test problems obtained with the method for N \~{} 102{\textendash}104 for different wave numbers are presented. {\textcopyright} 2005 Acoustical Society of America.}, keywords = {acoustic wave scattering, convergence of numerical methods, iterative methods, matrix multiplication}, doi = {10.1121/1.1853017}, url = {http://link.aip.org/link/?JAS/117/1744/1}, author = {Gumerov, Nail A. and Duraiswami, Ramani} } @article {14028, title = {Extracting the frequencies of the pinna spectral notches in measured head related impulse responses}, journal = {The Journal of the Acoustical Society of America}, volume = {118}, year = {2005}, month = {2005///}, pages = {364 - 374}, abstract = {The head related impulse response (HRIR) characterizes the auditory cues created by scattering of sound off a person{\textquoteright}s anatomy. The experimentally measured HRIR depends on several factors such as reflections from body parts (torso, shoulder, and knees), head diffraction, and reflection/diffraction effects due to the pinna. Structural models (Algazi et al., 2002; Brown and Duda, 1998) seek to establish direct relationships between the features in the HRIR and the anatomy. While there is evidence that particular features in the HRIR can be explained by anthropometry, the creation of such models from experimental data is hampered by the fact that the extraction of the features in the HRIR is not automatic. One of the prominent features observed in the HRIR, and one that has been shown to be important for elevation perception, are the deep spectral notches attributed to the pinna. In this paper we propose a method to robustly extract the frequencies of the pinna spectral notches from the measured HRIR, distinguishing them from other confounding features. The method also extracts the resonances described by Shaw (1997). The techniques are applied to the publicly available CIPIC HRIR database (Algazi et al., 2001c). The extracted notch frequencies are related to the physical dimensions and shape of the pinna.}, keywords = {acoustic wave reflection, acoustic wave scattering, anthropometry, Ear, hearing, physiological models}, doi = {10.1121/1.1923368}, url = {http://link.aip.org/link/?JAS/118/364/1}, author = {Raykar,Vikas C. and Duraiswami, Ramani and Yegnanarayana,B.} } @conference {14529, title = {Modeling the effect of a nearby boundary on the HRTF}, booktitle = {2001 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2001. Proceedings. (ICASSP {\textquoteright}01)}, volume = {5}, year = {2001}, month = {2001///}, pages = {3337-3340 vol.5 - 3337-3340 vol.5}, publisher = {IEEE}, organization = {IEEE}, abstract = {Understanding and simplified modeling of the head related transfer function (HRTF) holds the key to many applications in spatial audio. We develop an analytical solution to the problem of scattering of sound from a sphere in the vicinity of an infinite plane. Using this solution we study the influence of a nearby scattering rigid surface, on a spherical model for the HRTF}, keywords = {Acoustic scattering, acoustic signal processing, acoustic wave reflection, acoustic wave scattering, architectural acoustics, audio signal processing, Biological system modeling, boundary effect modeling, Computer interfaces, Ear, Educational institutions, Frequency, Head related transfer function, HRTF, HUMANS, infinite plane, Laboratories, Nails, Raman scattering, rigid surface, room environment, sound pressure level, sound scattering, spatial audio, sphere, spherical model, Transfer functions, wall influence}, isbn = {0-7803-7041-4}, doi = {10.1109/ICASSP.2001.940373}, author = {Gumerov, Nail A. and Duraiswami, Ramani} }