Jure Ravnik (Author), Leopold Škerget (Author), Zoran Žunič (Author)

Abstract

The boundary element method applied on non-homogenous partial differential equations requires calculation of a fully populated matrix of domain integrals. This paper compares two techniques: the fast multipole method and the fast wavelet transform, which are used to reduce the complexity of such domain matrices. The employed fast multipole method utilizes the expansion of integral kernels into series of spherical harmonics. The wavelet transform for vectors of arbitrary length, based on Haar wavelets and variable thresholding limit, is used. Both methods are tested and compared by solving the scalar Poisson equation and the velocity-vorticity vector kinematics equation. The results show comparable accuracy for both methods for a given data storage size. Wavelets are somewhat better for high and low compression ratios, and the fast multipole methods gives better results for moderate compressions. Considering implementation of the methods, the wavelet transform can easily be adapted for any problem, while the fast multipole method requires different expansion for each integral kernel.

Keywords

valčki;metoda hitrih multipolov;Poissonova enačba;metoda robnih elementov;wavelets;fast multipole method;Poisson equation;BEM;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UM FS - Faculty of Mechanical Engineering
UDC: 532
COBISS: 13062678 Link will open in a new window
ISSN: 0045-7825
Views: 1818
Downloads: 88
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Other data

Secondary language: English
Secondary keywords: valčki;metoda hitrih multipolov;Poissonova enačba;metoda robnih elementov;
URN: URN:SI:UM:
Pages: str. 1473-1485
Volume: ǂVol. ǂ198
Issue: ǂiss. ǂ17/20
Chronology: Apr. 2009
DOI: 10.1016/j.cma.2008.12.012
ID: 8716236