A Wavelet Galerkin Finite-Element Method for the Biot Wave Equation in the Fluid-Saturated Porous Medium | Zendy

Xinming Zhang | Zendy; Jiaqi Liu | Zendy; Liu Ke-an | Zendy

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A Wavelet Galerkin Finite-Element Method for the Biot Wave Equation in the Fluid-Saturated Porous Medium

Author(s) -

Xinming Zhang,

Jiaqi Liu,

Liu Ke-an

Publication year - 2009

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2009/142384

Subject(s) - wavelet , mathematics , mathematical analysis , cascade algorithm , daubechies wavelet , galerkin method , legendre wavelet , discrete wavelet transform , finite element method , wavelet transform , basis function , biot number , physics , computer science , mechanics , artificial intelligence , thermodynamics

A wavelet Galerkin finite-element method is proposed by combining the wavelet analysis with traditional finite-element method to analyze wave propagation phenomena in fluid-saturated porous medium. The scaling functions of Daubechies wavelets are considered as the interpolation basis functions to replace the polynomial functions, and then the wavelet element is constructed. In order to overcome the integral difficulty for lacking of the explicit expression for the Daubechies wavelets, a kind of characteristic function is introduced. The recursive expression of calculating the function values of Daubechies wavelets on the fraction nodes is deduced, and the rapid wavelet transform between the wavelet coefficient space and the wave field displacement space is constructed. The results of numerical simulation demonstrate that the method is effective

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