The wavelet-Galerkin method for solving PDE's with spatially dependent variables

Abstract : Discrete orthogonal wavelets are a family of functions with compact support which form a basis on a bounded domain. Use of these wavelet families as Galerkin trial functions for solving partial differential equations (PDE's) has been a topic of interest for the last decade, though research has primarily focused on equations with constant parameters. In the current paper the wavelet-Galerkin method is extended to allow spatial variation of equation parameters. A representative example from the field of vibration illustrates the method: compression waves in a bar with varying elastic modulus. The computed natural frequencies and modeshapes are compared to finite element solutions and show excellent correspondence. The wavelet-Galerkin method is also shown to be an efficient and convenient solution method as the majority of the calculations are performed a priori and can be stored for use in solving future PDE's. This efficiency is displayed by performing a stochastic analysis of elastic modulus variation to determine the effect on the frequency response function.
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Communication dans un congrès
19th International Congress on Sound and Vibration (ICSV19), Jul 2012, Lithuania. pp.R33 - numerical methods for acoustics and vibration - 326, 2012
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  • HAL Id : hal-00719744, version 1

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Simon Jones, Mathias Legrand. The wavelet-Galerkin method for solving PDE's with spatially dependent variables. 19th International Congress on Sound and Vibration (ICSV19), Jul 2012, Lithuania. pp.R33 - numerical methods for acoustics and vibration - 326, 2012. <hal-00719744>

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