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Fourier continuation methods for high-fidelity simulation of nonlinear acoustic beams

Albin, Nathan and Bruno, Oscar P. and Cheung, Theresa Y. and Cleveland, Robin O. (2012) Fourier continuation methods for high-fidelity simulation of nonlinear acoustic beams. Journal of the Acoustical Society of America, 132 (4). pp. 2371-2387. ISSN 0001-4966. doi:10.1121/1.4742722.

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On the basis of recently developed Fourier continuation (FC) methods and associated efficient parallelization techniques, this text introduces numerical algorithms that, due to very low dispersive errors, can accurately and efficiently solve the types of nonlinear partial differential equation (PDE) models of nonlinear acoustics in hundred-wavelength domains as arise in the simulation of focused medical ultrasound. As demonstrated in the examples presented in this text, the FC approach can be used to produce solutions to nonlinear acoustics PDEs models with significantly reduced discretization requirements over those associated with finite-difference, finite-element and finite-volume methods, especially in cases involving waves that travel distances that are orders of magnitude longer than their respective wavelengths. In these examples, the FC methodology is shown to lead to improvements in computing times by factors of hundreds and even thousands over those required by the standard approaches. A variety of one-and two-dimensional examples presented in this text demonstrate the power and capabilities of the proposed methodology, including an example containing a number of scattering centers and nonlinear multiple-scattering events.

Item Type:Article
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Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 2012 Acoustical Society of America. Received 12 November 2010; revised 25 May 2012; accepted 12 July 2012. N.A. gratefully acknowledges the support of the NSF postdoctoral fellowship. N.A. and O.P.B. gratefully acknowledge support from NSF and AFOSR. T.Y.C. and R.O.C. gratefully acknowledge support from NSF through grant 0835795.
Funding AgencyGrant Number
NSF Postdoctoral FellowshipUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Subject Keywords:acoustic wave scattering, biomedical ultrasonics, finite difference methods, finite element analysis, finite volume methods, Fourier analysis, nonlinear acoustics, partial differential equations
Issue or Number:4
Classification Code:PACS: 43.58.Ta; 43.80.Sh
Record Number:CaltechAUTHORS:20130103-105523405
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36143
Deposited By: Tony Diaz
Deposited On:09 Jan 2013 19:36
Last Modified:09 Nov 2021 23:20

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