A wavelet Galerkin finite-element method for the biot wave equation in the fluid-saturated porous medium
type: Item
instance of: scholarly article
title: A wavelet Galerkin finite-element method for the biot wave equation in the fluid-saturated porous medium
zbMATH Open document ID: 1180.76036
DOI: 10.1155/2009/142384
author: Jiaqi Liu
author: Ke'an Liu
author: Xin-Ming Zhang
published in: Mathematical Problems in Engineering
publication date: 2009-11-13T00:00:00Z
full work available at URL: https://eudml.org/doc/45796
review text: Summary: 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.
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 76S05
zbMATH DE Number: 5632438
Wikidata QID: Q58648878
MaRDI profile type: Publication
OpenAlex ID: W2075915355
cites work: Symmetric wave propagation in a fluid-saturated incompressible porous medium
cites work: An analytical solution for the transient response of saturated porous elastic solids
cites work: Evaluation ofu -w andu - π finite element methods for the dynamic response of saturated porous media using one-dimensional models
cites work: Q4248811
cites work: Orthonormal bases of compactly supported wavelets
cites work: Q4027569
cites work: A class of finite element methods based on orthonormal, compactly supported wavelets
cites work: Using the Refinement Equation for Evaluating Integrals of Wavelets
cites work: Applications of wavelet Galerkin FEM to bending of beam and plate structures
cites work: Transient wave propagation in a one-dimensional poroelastic column
description: scientific article; zbMATH DE number 5632438