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Comparison between the shifted-Laplacian preconditioning and the controllability methods for computational acoustics

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Airaksinen, T., & Mönkölä, S. (2010). Comparison between the shifted-Laplacian preconditioning and the controllability methods for computational acoustics. Journal of Computational and Applied Mathematics, 234(6), 1796-1802. https://doi.org/10.1016/j.cam.2009.08.030
Published in
Journal of Computational and Applied Mathematics
Authors
Airaksinen, Tuomas |
Mönkölä, Sanna
Date
2010
Discipline
TietotekniikkaMathematical Information Technology
Copyright
© Elsevier

 
Processes that can be modelled with numerical calculations of acoustic pressure fields include medical and industrial ultrasound, echo sounding, and environmental noise. We present two methods for making these calculations based on Helmholtz equation. The first method is based directly on the complex-valued Helmholtz equation and an algebraic multigrid approximation of the discretized shifted-Laplacian operator; i.e. the damped Helmholtz operator as a preconditioner. The second approach returns to a transient wave equation, and finds the time-periodic solution using a controllability technique. We concentrate on acoustic problems, but our methods can be used for other types of Helmholtz problems as well. Numerical experiments show that the control method takes more CPU time, whereas the shifted-Laplacian method has larger memory requirement.
Publisher
Elsevier
Keywords
Helmholtz equation Computational acoustics Algebraic multigrid method Preconditioner Exact controllability Finite element method Spectral element method
DOI
https://doi.org/10.1016/j.cam.2009.08.030
URI

http://urn.fi/URN:NBN:fi:jyu-20112211791

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/19276827

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  • Informaatioteknologian tiedekunta [1793]

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