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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article; Proceedings Paper

Airaksinen, Tuomas¹  Monkola, Sanna¹ 

[1] Univ Jyvaskyla, Dept Math Informat Technol, FI-40014 Jyvaskyla, Finland

关键词: Helmholtz equation;    Computational acoustics;    Algebraic multigrid method;    Preconditioner;    Exact controllability;    Finite element method;    Spectral element method;   

DOI  :  10.1016/j.cam.2009.08.030

来源: Elsevier

【 摘 要 】

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. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free