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

← Back to Volume 35, No. 2