TY - JOUR
T1 - A k-space method for moderately nonlinear wave propagation
AU - Jing, Yun
AU - Wang, Tianren
AU - Clement, Greg T.
N1 - Funding Information:
Manuscript received december 28, 2011; accepted april 22, 2012. This work was partially supported by national Institutes of Health grant number U41rr019703. y. Jing and T. Wang are with the department of Mechanical and aerospace Engineering, north carolina state University, raleigh, nc (e-mail: [email protected]). g. T. clement is with the department of radiology, Brigham and Women’s Hospital, Harvard Medical school, Boston, Ma. doI http://dx.doi.org/10.1109/TUFFc.2012.2372
PY - 2012
Y1 - 2012
N2 - A k-space method for moderately nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to analytic solutions and finite-difference time-domain (FDTD) method. It is found that to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant-Friedrichs-Lewy number can be as large as 0.4. Through comparisons with the conventional FDTD method, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient and accurate. The k-space method is then employed to study three-dimensional nonlinear wave propagation through the skull, which shows that a relatively accurate focusing can be achieved in the brain at a high frequency by sending a low frequency from the transducer. Finally, implementations of the k-space method using a single graphics processing unit shows that it required about one-seventh the computation time of a single-core CPU calculation.
AB - A k-space method for moderately nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to analytic solutions and finite-difference time-domain (FDTD) method. It is found that to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant-Friedrichs-Lewy number can be as large as 0.4. Through comparisons with the conventional FDTD method, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient and accurate. The k-space method is then employed to study three-dimensional nonlinear wave propagation through the skull, which shows that a relatively accurate focusing can be achieved in the brain at a high frequency by sending a low frequency from the transducer. Finally, implementations of the k-space method using a single graphics processing unit shows that it required about one-seventh the computation time of a single-core CPU calculation.
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U2 - 10.1109/TUFFC.2012.2372
DO - 10.1109/TUFFC.2012.2372
M3 - Article
C2 - 22899114
AN - SCOPUS:84865402729
SN - 0885-3010
VL - 59
SP - 1664
EP - 1673
JO - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
JF - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
IS - 8
M1 - 6264131
ER -