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Structural Engineering and Mechanics
  Volume 35, Number 2, May30 2010 , pages 175-190
DOI: https://doi.org/10.12989/sem.2010.35.2.175
 


New decoupled wavelet bases for multiresolution structural analysis
Youming Wang, Xuefeng Chen, Yumin He and Zhengjia He

 
Abstract
    One of the intractable problems in multiresolution structural analysis is the decoupling computation between scales, which can be realized by the operator-orthogonal wavelets based on the lifting scheme. The multiresolution finite element space is described and the formulation of multiresolution finite element models for structural problems is discussed. Various operator-orthogonal wavelets are constructed by the lifting scheme according to the operators of multiresolution finite element models. A dynamic multiresolution algorithm using operator-orthogonal wavelets is proposed to solve structural problems. Numerical examples demonstrate that the lifting scheme is a flexible and efficient tool to construct operator-orthogonal wavelets for multiresolution structural analysis with high convergence rate.
 
Key Words
    multiresolution finite element; lifting scheme; operator-orthogonal wavelet.
 
Address
Youming Wang: State Key Lab for Manufacturing Systems Engineering, Xi\'an Jiaotong University, Xi\'an 710049, People\'s Republic of China
Xuefeng Chen: State Key Lab for Manufacturing Systems Engineering, Xi\'an Jiaotong University, Xi\'an 710049, People\'s Republic of China
Yumin He: State Key Lab for Manufacturing Systems Engineering, Xi\'an Jiaotong University, Xi\'an 710049, People\'s Republic of China
Zhengjia He: State Key Lab for Manufacturing Systems Engineering, Xi\'an Jiaotong University, Xi\'an 710049, People\'s Republic of China
 

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