Obtaining head-related transfer functions (HRTFs) is a challenging task, in spite of its importance in localizing sound in a three-dimensional (3D) environment or improving the performance of hearing aids, among their various applications. In this paper, an optimized finite element method through adaptive dimension size based on wavelength (frequency) for acoustic scattering analyses using ansys is presented. Initial investigation of the validity of our method is conducted by simulating scattered sound field for a solid sphere exposed to a far-field plane sound wave at 100 (equally spaced in logarithmic scale) frequencies between 20 and 20 kHz. Comparison of the equivalent HRTF results between the two methods shows a maximum deviation of less than 0.6 dB between our method and the analytical solution depending on the angle of rotation of the sphere with respect to sound source.

References

1.
Xie
,
B.
,
2013
,
Head-Related Transfer Function and Virtual Auditory Display
,
J. Ross Publishing
, Plantation, FL.
2.
Potisk
,
T.
,
2015
, “
Head-Related Transfer Function
,” Seminar Ia, Faculty of Mathematics and Physics,
University of Ljubljana
, Ljubljana, Slovenia.
3.
Algazi
, V
. R.
,
Duda
,
R. O.
,
Duraiswami
,
R.
,
Gumerov
,
N. A.
, and
Tang
,
Z.
,
2002
, “
Approximating the Head-Related Transfer Function Using Simple Geometric Models of the Head and Torso
,”
J. Acoust. Soc. Am.
,
112
(
5
), pp.
2053
2064
.
4.
Fallahi
,
M.
,
Brinkmann
,
F.
, and
Weinzierl
,
S.
,
2015
, “
Simulation and Analysis of Measurement Techniques for the Fast Acquisition of Head-Related Transfer Functions
,”
German Annual Conference on Acoustics
(
DAGA
), Nuremberg, Germany, Mar. 16–19, pp. 1107–1110.
5.
Zotkin
,
D. N.
,
Duraiswami
,
R.
,
Grassi
,
E.
, and
Gumerov
,
N. A.
,
2006
, “
Fast Head-Related Transfer Function Measurement Via Reciprocity
,”
J. Acoust. Soc. Am.
,
120
(
4
), pp.
2202
2215
.
6.
Kuester
,
E. F.
, and
Holloway
,
C. L.
,
1994
, “
A Low-Frequency Model for Wedge or Pyramid Absorber Arrays—I: Theory
,”
IEEE Trans. Electromagn. Compat.
,
36
(
4
), pp.
300
306
.
7.
Katz
,
B. F.
,
2001
, “
Boundary Element Method Calculation of Individual Head-Related Transfer Function—I: Rigid Model Calculation
,”
J. Acoust. Soc. Am.
,
110
(
5
), pp.
2440
2448
.
8.
Harder
,
S.
,
Paulsen
,
R. R.
,
Larsen
,
M.
,
Laugesen
,
S.
,
Mihocic
,
M.
, and
Majdak
,
P.
,
2016
, “
A Framework for Geometry Acquisition, 3-D Printing, Simulation, and Measurement of Head-Related Transfer Functions With a Focus on Hearing-Assistive Devices
,”
Comput. Aided Des.
,
75–76
, pp.
39
46
.
9.
Kreuzer
,
W.
,
Majdak
,
P.
, and
Chen
,
Z.
,
2009
, “
Fast Multipole Boundary Element Method to Calculate Head-Related Transfer Functions for a Wide Frequency Range
,”
J. Acoust. Soc. Am.
,
126
(
3
), pp.
1280
1290
.
10.
Kahana
,
Y.
,
2000
, “
Numerical Modelling of the Head-Related Transfer Function
,” Ph.D. thesis, University of Southampton, Southampton, UK.
11.
Bolejko
,
R.
, and
Dobrucki
,
A.
,
2006
, “
FEM and BEM Computing Costs for Acoustical Problems
,”
Arch. Acoust.
,
31
(
2
), pp.
193
212
.
12.
Atalla
,
N.
, and
Sgard
,
F.
,
2015
,
Finite Element and Boundary Methods in Structural Acoustics and Vibration
,
CRC Press
, Boca Raton, FL.
13.
Mokhtari
,
P.
,
Nishimura
,
R.
, and
Takemoto
,
H.
,
2008
, “
Toward HRTF Personalization: An Auditory-Perceptual Evaluation of Simulated and Measured HRTFS
,” International Conference on Auditory Display (
ICAD
), Paris, France, June 24–27, pp. ICAD08-1–ICAD08-8.
14.
Mokhtari
,
P.
,
Takemoto
,
H.
,
Nishimura
,
R.
, and
Kato
,
H.
,
2008
, “
Efficient Computation of HRTFS at any Distance by FDTD Simulation With Near to far Field Transformation
,”
Autumn Meeting of the Acoustic Society of Japan
, pp.
611
614
.
15.
Bates
,
A. P.
,
Khalid
,
Z.
, and
Kennedy
,
R. A.
,
2015
, “
On the Use of Slepian Functions for the Reconstruction of the Head-Related Transfer Function on the Sphere
,”
9th International Conference on Signal Processing and Communication Systems
(
ICSPCS
), Cairns, Queensland, Australia, Dec. 14–16, pp.
1
7
.
16.
Trevino
,
J.
,
Hu
,
S.
,
Salvador
,
C.
,
Sakamoto
,
S.
,
Li
,
J.
, and
Suzuki
,
Y.-O.
,
2015
, “
A Compact Representation of the Head-Related Transfer Function Inspired by the Wavelet Transform on the Sphere
,”
International Conference on Intelligent Information Hiding and Multimedia Signal Processing
(
IIH-MSP
), Adelaide, Australia, Sept. 23–25, pp.
372
375
.
17.
Howard
,
C. Q.
, and
Cazzolato
,
B. S.
,
2014
,
Acoustic Analyses Using Matlab® and Ansys®
,
CRC Press
, Boca Raton, FL.
18.
Kaltenbacher
,
M.
,
Escobar
,
M.
,
Becker
,
S.
, and
Ali
,
I.
,
2010
, “
Numerical Simulation of Flow-Induced Noise Using LES/SAS and Lighthill's Acoustic Analogy
,”
Int. J. Numer. Methods Fluids
,
63
(
9
), pp.
1103
1122
.
19.
Kaltenbacher
,
M.
,
2007
,
Numerical Simulation of Mechatronic Sensors and Actuators
, Vol.
2
,
Springer
, Berlin.
20.
Mach
,
M.
, and
Summer
,
R.
,
2005
, “
Some Aspects of Investigation of Magnetic Fields Produced by Medium Voltage Switchgears
,”
3rd International Scientific Symposium on Electric Power Engineering
(
ELEKTROENERGETIKA
), Stara Lesna, Slovakia, Sept. 21–23, pp. 487–495.
21.
Noreika
,
A.
, and
Tarvydas
,
P.
,
2007
, “
Analysis of Finite Element Method Equation Solvers
,”
29th International Conference on Information Technology Interfaces
(
ITI
), Dubrovnik, Croatia, June 25–28, pp.
633
638
.
22.
Jacobsen
,
F.
, and
Juhl
,
P. M.
,
2013
,
Fundamentals of General Linear Acoustics
,
Wiley
, Chichester, UK.
23.
Turley
,
S.
,
2006
, “
Acoustic Scattering From a Sphere
,”
Class Notes, Department of Physics and Astronomy, Brigham Young University
.
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