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

✍ Scribed by Tuomas Airaksinen; Sanna Mönkölä

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
792 KB
Volume
234
Category
Article
ISSN
0377-0427

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✦ Synopsis

Finite element method Spectral element method a b s t r a c t 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.

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