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Controllability method for the Helmholtz equation with higher-order discretizations

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Heikkola, E., Mönkölä, S., Pennanen, A., & Rossi, T. (2007). Controllability method for the Helmholtz equation with higher-order discretizations. Journal of Computational Physics, 225(2), 1553-1576. https://doi.org/10.1016/j.jcp.2007.02.003
Published in
Journal of Computational Physics
Authors
Heikkola, Erkki |
Mönkölä, Sanna |
Pennanen, Anssi |
Rossi, Tuomo
Date
2007
Copyright
© Elsevier. This is an author's final draft version of an article whose final and definitive form has been published by Elsevier.

 
We consider a controllability technique for the numerical solution of the Helmholtz equation. The original time-harmonic equation is represented as an exact controllability problem for the time-dependent wave equation. This problem is then formulated as a least-squares optimization problem, which is solved by the conjugate gradient method. Such an approach was first suggested and developed in the 1990s by French researchers and we introduce some improvements to its practical realization. We use higher-order spectral elements for spatial discretization, which leads to high accuracy and lumped mass matrices. Higher-order approximation reduces the pollution effect associated with finite element approximation of time-harmonic wave equations, and mass lumping makes explicit time-stepping schemes for the wave equation very efficient. We also derive a new way to compute the gradient of the least-squares functional and use algebraic multigrid method for preconditioning the conjugate gradient algorithm. Numerical results demonstrate the significant improvements in efficiency due to the higher-order spectral elements. For a given accuracy, spectral element method requires fewer computational operations than conventional finite element method. In addition, by using higher-order polynomial basis the influence of the pollution effect is reduced. ...
Publisher
Elsevier
ISSN Search the Publication Forum
0021-9991
Keywords
akustinen sironta
DOI
https://doi.org/10.1016/j.jcp.2007.02.003
URI

http://urn.fi/URN:NBN:fi:jyu-201210102638

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/16832188

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  • Informaatioteknologian tiedekunta [1807]

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