Controllability method for acoustic scattering with spectral elements

Abstrakti
We formulate the Helmholtz equation as an exact controllability problem for the time-dependent wave equation. The problem is then discretized in time domain with central finite difference scheme and in space domain with spectral elements. This approach leads to high accuracy in spatial discretization. Moreover, the spectral element method results in diagonal mass matrices, which makes the time integration of the wave equation highly efficient. After discretization, the exact controllability problem is reformulated as a least-squares problem, which is solved by the conjugate gradient method. We illustrate the method with some numerical experiments, which demonstrate the significant improvements in efficiency due to the higher order spectral elements. For a given accuracy, the controllability technique with spectral element method requires fewer computational operations than with conventional finite element method. In addition, by using higher order polynomial basis the influence of the pollution effect is reduced.
Päätekijät
Aineistotyyppi
Artikkelit Tutkimusartikkeli
Julkaistu
2007
Sarja
Aiheet
Julkaisu tutkimustietojärjestelmässä
Julkaisija
Elsevier
Julkaisun pysyvä osoite
https://urn.fi/URN:NBN:fi:jyu-201210102637Käytä tätä linkitykseen
Vertaisarvioinnin tila
Vertaisarvioitu
ISSN
0377-0427
DOI
https://doi.org/10.1016/j.cam.2006.02.046
Kieli
englanti
Julkaisussa
Journal of Computational and Applied Mathematics
Viite
  • Heikkola, E., Mönkölä, S., Pennanen, A., & Rossi, T. (2007). Controllability method for acoustic scattering with spectral elements. Journal of Computational and Applied Mathematics, 204(2), 344-355. https://doi.org/10.1016/j.cam.2006.02.046
Lisenssi
Open Access
Copyright© Elsevier. This is an author's final draft version of an article whose final and definitive form has been published by Elsevier.

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