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.