A k-space method for moderately nonlinear wave propagation

Yun Jing, Tianren Wang, Greg T. Clement

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

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.

Original languageEnglish (US)
Article number6264131
Pages (from-to)1664-1673
Number of pages10
JournalIEEE transactions on ultrasonics, ferroelectrics, and frequency control
Volume59
Issue number8
DOIs
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Instrumentation
  • Acoustics and Ultrasonics
  • Electrical and Electronic Engineering

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