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    Construction of Operator-Orthogonal Wavelet-Based Elements for Adaptive Analysis of Thin Plate Bending Problems

    Y.M. Wang1,2, Q. Wu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.1, pp. 17-45, 2013, DOI:10.3970/cmes.2013.093.017

    Abstract A new kind of operator-orthogonal wavelet-based element is constructed based on the lifting scheme for adaptive analysis of thin plate bending problems. The operators of rectangular and skew thin plate bending problems and the sufficient condition for the operator-orthogonality of multilevel stiffness matrix are derived in the multiresolution finite element space. A new type of operator-orthogonal wavelets for thin plate bending problems is custom designed with high vanishing moments to be orthogonal with the scaling functions with respect to the operators of the problems, which ensures the independent solution of the problems in each scale. An adaptive operator-orthogonal wavelet method… More >

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