A fast wavelet-multigrid method to solve elliptic partial differential equations

Bujurke, N. M.; Salimath, C. S.; Kudenatti, Ramesh B.; Shiralashetti, S. C.

doi:10.1016/j.amc.2006.07.074

Cited by 25 publications

(13 citation statements)

References 17 publications

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“…From the more recent papers we cite here the following. Bujurke et al [3], Schwab and Stevenson [13] applied wavelet algorithms for solving boundary value problems for elliptic PDEs. Chen et al [5] studied multiscale wavelet-based elements for adaptive finite element analysis.…”

Section: Related Papersmentioning

confidence: 99%

Solving PDEs with the Aid of Two-Dimensional Haar Wavelets

Lepik

2014

Mathematical Engineering

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Section: Related Papersmentioning

confidence: 99%

Solving PDEs with the Aid of Two-Dimensional Haar Wavelets

Lepik

2014

Mathematical Engineering

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“…If we combine these inherent multiresolution properties with multigrid ideas, then it enables one to reduce the computation time and simplify the implementation procedure [20,21]. We employ, in this direction, a modified V-cycle in which intergrid operators in the V-cycle of the classical multigrid scheme are replaced by forward and inverse wavelet transforms [22].…”

Section: Wavelet-multigrid Approachmentioning

confidence: 99%

Analysis of modified Reynolds equation using the wavelet‐multigrid scheme

Bujurke

Salimath

Kudenatti

et al. 2006

Numerical Methods Partial

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The combined study of effects of surface roughness and poroelasticity on the squeeze film behavior of bearings in general and that of synovial joints in particular are presented. The modified form of Reynolds equation, which incorporates the randomized roughness structure as well as elastic nature of articular cartilage, is derived. Christensen stochastic theory describing roughness structure of cartilage surfaces is used by assuming the roughness asperity heights to be small compared to the film thickness. A recently developed wavelet-multigrid method is used for the solution of Reynolds equation. The method has the greatest advantage of minimizing the errors using wavelet transforms in obtaining accurate solution, as grid size tends to zero. Based on the results obtained, the influence of roughness and elasticity on bearing characteristics are discussed in some detail.

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“…Wavelets represent a newly developed powerful mathematical tool, which has been broadly applied to signal decompositions and reconstructions, Laplace inversions [13] and differential equation solutions [14,15] etc. Wavelets are defined by the wavelet function and scaling function in the real line, which are in effect a band-pass and low-pass filter.…”

Section: Introductionmentioning

confidence: 99%

A wavelet approach for active-passive vibration control of laminated plates

Wang

Zhou

2012

Acta Mech Sin

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As an extension of the wavelet approach to vibration control of piezoelectric beam-type plates developed earlier by the authors, this paper proposes a hybrid activepassive control strategy for suppressing vibrations of laminated rectangular plates bonded with distributed piezoelectric sensors and actuators via thin viscoelastic bonding layers. Owing to the low-pass filtering property of scaling function transform in orthogonal wavelet theory, this waveletbased control method has the ability to automatically filter out noise-like signal in the feedback control loop, hence reducing the risk of residual coupling effects which are usually the source of spillover instability. Moreover, the existence of thin viscoelastic bonding layers can further improve robustness and reliability of the system through dissipating the energy of any other possible noise induced partially by numerical errors during the control process. A simulation procedure based on an advanced wavelet-Galerkin technique is suggested to realize the hybrid active-passive control process. Numerical results demonstrate the efficiency of the proposed approach.

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A fast wavelet-multigrid method to solve elliptic partial differential equations

Cited by 25 publications

References 17 publications

Solving PDEs with the Aid of Two-Dimensional Haar Wavelets

Solving PDEs with the Aid of Two-Dimensional Haar Wavelets

Analysis of modified Reynolds equation using the wavelet‐multigrid scheme

A wavelet approach for active-passive vibration control of laminated plates

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