The Multiscale Hybrid Mixed Method for the Helmholtz Equation.

Abstract : The numerical simulation of wave propagation in heterogeneous media comes with two main difficulties. On the one hand, when solving for high frequencies, the so called pollution effect forces the use of fine meshes, or high order methods. On the other hand, strongly heterogeneous media, requires the mesh to fit the heterogeneity contrasts, making high order polynomials unefficient. The Multiscale Hybrid Mixed (MHM) method has been shown to be extremely powerful to deal with strongly heterogeneous media on a coarse mesh, in the context of elliptic problems. In order to handle high contrasts within a cell, heteregoneities-adapted shape functions, are localy computed. Those shape functions are then used in a global problem on the coarse mesh. In this work, we apply the MHM methodology to the Helmholtz equation in homogeneous media (we think of the homogeneous case as a first step before adressing heterogeneous media). The general MHM methodology, and its application to the particular case of the Helmholtz equation will be discussed. Numerical experiments, assessing the convergence of the method, as well as comparisons with the standard Finite Element Method (FEM), will be presented. It turns out that the MHM method enables the use of coarse mesh even at high frequencies, the oscillations of the solution being captured by the localy computed shape functions, thus reducing the number of degrees of freedom in the global problem compared to the classical FEM.
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Contributor : Théophile Chaumont Frelet <>
Submitted on : Tuesday, January 14, 2014 - 1:17:59 PM
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  • HAL Id : hal-00930139, version 1


Hélène Barucq, Henri Calandra, Théophile Chaumont Frelet, Christian Gout, Frédéric Valentin. The Multiscale Hybrid Mixed Method for the Helmholtz Equation.. HOSCAR - 3rd Brazil-French workshop on High performance cOmputing and SCientific dAta management dRiven by highly demanding applications (INRIA-CNPq) (2013), Sep 2013, Bordeaux, France. ⟨hal-00930139⟩



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