Author(s)

Rodrigo Bird Burgos¹, Marco Antonio Cetale Santos²

¹Department of Structures and Foundations, Rio de Janeiro State University (UERJ), Rio de Janeiro, Brazil.
²Department of Geology and Geophysics, Fluminense Federal University (UFF), Niterói, Brazil.

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.

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

Burgos, R. and Santos, M. (2016) Finite Elements Based on Deslauriers-Dubuc Wavelets for Wave Propagation Problems. Applied Mathematics, 7, 1490-1497. doi: 10.4236/am.2016.714128.