New decoupled wavelet bases for multiresolution structural analysis

Youming Wang , Xuefeng Chen , Yumin He , 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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