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**Hat interpolation wavelet-based multi-scale Galerkin method for thin-walled box beam analysis.**
*(English)*
Zbl 1114.74503

Summary: The objective of the present work is to propose a new adaptive wavelet-Galerkin method based on the lowest-order hat interpolation wavelets. The specific application of the present method is made on the one-dimensional analysis of thin-walled box beam problems exhibiting rapidly varying local end effects. Higher-order interpolation wavelets have been used in the wavelet-collocation setting, but the lowest-order hat interpolation is applied here first and a hat interpolation wavelet-based Galerkin method is newly formulated. Unlike existing orthogonal or biorthogonal wavelet-based Galerkin methods, the present method does not require special treatment in dealing with general boundary conditions. Furthermore, the present method directly works with nodal values and does not require special formula for the evaluation of system matrices. Though interpolation wavelets do not have any vanishing moment, an adaptive scheme based on multi-resolution approximations is possible and a preconditioned conjugate gradient method can be used to enhance numerical efficiency.

### MSC:

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

65T60 | Numerical methods for wavelets |

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\textit{Y. Y. Kim} and \textit{G.-W. Jang}, Int. J. Numer. Methods Eng. 53, No. 7, 1575--1592 (2002; Zbl 1114.74503)

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