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Relevant numerical methods for mesoscale wave propagation in heterogeneous media

Abstract : This thesis work deals with a posteriori error estimates for finite element solutions of the elastic wave equation in heterogeneous media. Two different a posteriori estimation approaches are developed. The first one, in a classical way, considers directly the elastodynamic equation and results in a new explicit error estimator in a non-natural L∞ norm in time. Its key features are the use of the residual method and the development of space and time reconstructions with respect to regularities required by different residual operators contributing to the proposed error bound. Numerical applications of the error bound with different mesh sizes show that it gives rise to a fully computable upper bound. However, its effectivity index and its asymptotic accuracy remain to be improved. The second error estimator is derived for high frequency wave propagation problem in heterogeneous media in the weak coupling regime. It is a new residual-type error based on the radiative transfer equation, which is derived by a multi-scale asymptotic expansion of the wave equation in terms of the spatio-temporal Wigner transforms of wave fields. The residual errors are in terms of angularly resolved energy quantities of numerical solutions of waves by finite element method. Numerical calculations of the defined errors in 1D homogeneous and heterogeneous media allow validating the proposed error estimation approach. The application field of this work is the numerical modelling of the seismic wave propagation in geophysical media or the ultrasonic wave propagation in polycrystalline materials.
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Submitted on : Friday, July 20, 2018 - 3:49:22 PM
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  • HAL Id : tel-01845764, version 1


Wen Wu. Relevant numerical methods for mesoscale wave propagation in heterogeneous media. Mechanics of the solides [physics.class-ph]. Université Paris-Saclay, 2018. English. ⟨NNT : 2018SCALC044⟩. ⟨tel-01845764⟩



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