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Optimized meshfree methods for acoustics
Publikationstyp
Journal Article
Date Issued
2011-03-30
Sprache
English
Author(s)
Institut
Volume
200
Issue
25-28
Start Page
2223
End Page
2236
Citation
Computer Methods in Applied Mechanics and Engineering 200 (25-28): 2223-2236 (2011)
Publisher DOI
Scopus ID
Publisher
Elsevier Science
When the Helmholtz equation is solved by numerical methods as, e.g., the finite element method (FEM), the solution suffers from the so-called pollution effect. The pollution is mainly caused by the dispersion, meaning that the numerical wave number disagrees with the wave number of the exact solution. This leads to inaccurate results, especially for high wave numbers. In order to obtain acceptable results also for higher wave numbers, either a high element resolution or elements of a higher order can be used. For either option the consequence is an increased computation time and memory capacity. Meshfree methods as the element free Galerkin method (EFGM) and the radial point interpolation method (RPIM) are not dispersion-free either, but it has been shown that meshfree methods are able to reduce the dispersion significantly. Both methods offer several parameters, which can be modified in order to obtain optimal results with respect to the dispersion effect. This work presents an exhaustive parameter study on both the EFGM and the RPIM. It is shown, that the methods can be significantly improved if certain parameters as, e.g., weighting functions, shape parameters, size of the influence domain, are chosen appropriately.
Subjects
Acoustics
Dispersion
EFGM
Helmholtz equation
Meshfree methods
RPIM
DDC Class
530: Physik
600: Technik
620: Ingenieurwissenschaften