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Comparison between wavelet and fast multipole data sparse approximations for Poisson and kinematics boundary - domain integral equations
Jure Ravnik, Leopold Škerget, Zoran Žunič, 2009, izvirni znanstveni članek

Opis: 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.
Ključne besede: wavelets, fast multipole method, Poisson equation, BEM
Objavljeno v DKUM: 31.05.2012; Ogledov: 2440; Prenosov: 108
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Characterization of corrosion processes by current noise wavelet-based fractaland correlation analysis
Peter Planinšič, Aljana Petek, 2008, izvirni znanstveni članek

Opis: Electrochemical noise data in the presence of pitting, general corrosion and passivity were analyzed using the discrete wavelet transform. The registered current noise was decomposed into a set of band-limited details, which contain information about corrosion events occurring at a determined time-scale. It has been observed that the signal variance and variances of details depend on the intensity of processes. Distribution of the signal energy among different details was characteristic for the particular type of corrosion. The characterization of corrosion processes on the basis of in the wavelet domain calculated Hurst parameter H and fractal dimension, D, of electrochemical noise signals has been established. It is concluded that general corrosion is a stationary random process with a weak persistence and D= 2.14, whereas pitting corrosion is a non-stationary process with a long memory effect and D = 1.07. Passivity is a non-stationary process near to the Brownian motion with D = 1.56. The persistence features of electrochemical noise signals were explained also by correlation coefficients calculated between signals obtained by discrete wavelet multiresolution decomposition.
Ključne besede: elektrokemijski šum, valčki, Hurstov parameter, fraktalna dimenzija, korelacijski koeficient, korozija, electrochemical noise, wavelets, Hurst parameter, fractal dimension, correlation coefficients, corrosion
Objavljeno v DKUM: 31.05.2012; Ogledov: 2338; Prenosov: 89
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