@article {13963,
	title = {Computation of the head-related transfer function via the fast multipole accelerated boundary element method and its spherical harmonic representation},
	journal = {The Journal of the Acoustical Society of America},
	volume = {127},
	year = {2010},
	month = {2010///},
	pages = {370 - 386},
	abstract = {The head-related transfer function (HRTF) is computed using the fast multipole accelerated boundary element method. For efficiency, the HRTF is computed using the reciprocity principle by placing a source at the ear and computing its field. Analysis is presented to modify the boundary value problem accordingly. To compute the HRTF corresponding to different ranges via a single computation, a compact and accurate representation of the HRTF, termed the spherical spectrum, is developed. Computations are reduced to a two stage process, the computation of the spherical spectrum and a subsequent evaluation of the HRTF. This representation allows easy interpolation and range extrapolation of HRTFs. HRTF computations are performed for the range of audible frequencies up to 20 kHz for several models including a sphere, human head models [the Neumann KU-100 ({\textquotedblleft}Fritz{\textquotedblright}) and the Knowles KEMAR ({\textquotedblleft}Kemar{\textquotedblright}) manikins], and head-and-torso model (the Kemar manikin). Comparisons between the different cases are provided. Comparisons with the computational data of other authors and available experimental data are conducted and show satisfactory agreement for the frequencies for which reliable experimental data are available. Results show that, given a good mesh, it is feasible to compute the HRTF over the full audible range on a regular personal computer.},
	keywords = {auditory evoked potentials, bioacoustics, boundary-elements methods, Ear, Harmonic analysis},
	doi = {10.1121/1.3257598},
	url = {http://link.aip.org/link/?JAS/127/370/1},
	author = {Gumerov, Nail A. and O{\textquoteright}Donovan,Adam E. and Duraiswami, Ramani and Zotkin,Dmitry N}
}
@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}
}
@conference {18458,
	title = {Fast Multipole Accelerated Boundary Elements for Numerical Computation of the Head Related Transfer Function},
	booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing, 2007. ICASSP 2007},
	volume = {1},
	year = {2007},
	month = {2007/04//},
	pages = {I-165-I-168 - I-165-I-168},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {The numerical computation of head related transfer functions has been attempted by a number of researchers. However, the cost of the computations has meant that usually only low frequencies can be computed and further the computations take inordinately long times. Because of this, comparisons of the computations with measurements are also difficult. We present a fast multipole based iterative preconditioned Krylov solution of a boundary element formulation of the problem and use a new formulation that enables the reciprocity technique to be accurately employed. This allows the calculation to proceed for higher frequencies and larger discretizations. Preliminary results of the computations and of comparisons with measured HRTFs are presented.},
	keywords = {Acceleration, Acoustic measurements, Acoustic scattering, audio signal processing, boundary element formulation, Boundary element method, Boundary element methods, boundary-elements methods, Costs, Ear, Fast Multipole Method, Frequency, Head related transfer function, HUMANS, Irrigation, iterative methods, multipole accelerated boundary elements, multipole based iterative preconditioned Krylov solution, numerical computation, Reciprocity, Transfer functions},
	isbn = {1-4244-0727-3},
	doi = {10.1109/ICASSP.2007.366642},
	author = {Gumerov, Nail A. and Duraiswami, Ramani and Zotkin,Dmitry N}
}
