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Latto, A., Resnikoff, H.L. and Tenenbaum, E. (1992) The Evaluation of Connection Coefficients of Compactly Supported Wavelets. In: Maday, Y., Ed., Proceedings of the French-USA Workshop on Wavelets and Turbulence, Princeton University, June 1991, Springer-Verlag, New York, 76-89.

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• TITLE: Finite Elements Based on Deslauriers-Dubuc Wavelets for Wave Propagation Problems

  AUTHORS: Rodrigo Bird Burgos, Marco Antonio Cetale Santos

  KEYWORDS: Wavelets, Interpolets, Deslauriers-Dubuc, Wavelet Finite Element Method, Wave Propagation

  JOURNAL NAME: Applied Mathematics, Vol.7 No.14, August 17, 2016

  ABSTRACT: This paper presents the formulation of finite elements based on Deslauriers-Dubuc interpolating scaling functions, also known as Interpolets, for their use in wave propagation modeling. Unlike other wavelet families like Daubechies, Interpolets possess rational filter coefficients, are smooth, symmetric and therefore more suitable for use in numerical methods. Expressions for stiffness and mass matrices are developed based on connection coefficients, which are inner products of basis functions and their derivatives. An example in 1-D was formulated using Central Difference and Newmark schemes for time differentiation. Encouraging results were obtained even for large time steps. Results obtained in 2-D are compared with the standard Finite Difference Method for validation.