Stability analysis of heterogeneous Helmholtz problems and finite element solution based on propagation media approximation

Abstract : The numerical simulation of time-harmonic waves in heterogeneous media is a tricky task which consists in reproducing oscillations. These oscillations become stronger as the frequency increases, and high-order finite element methods have demonstrated their capability to reproduce the oscilla-tory behavior. However, they keep coping with limitations in capturing fine scale heterogeneities. We propose a new approach which can be applied in highly heterogeneous propagation media. It consists in constructing an approximate medium in which we can perform computations for a large variety of frequencies. The construction of the approximate medium can be understood as applying a quadrature formula locally. We establish estimates which generalize existing estimates formerly obtained for homogeneous Helmholtz problems. We then provide numerical results which illustrate the good level of accuracy of our solution methodology.
Complete list of metadatas

Cited literature [28 references]  Display  Hide  Download

https://hal.inria.fr/hal-01408934
Contributor : Théophile Chaumont-Frelet <>
Submitted on : Monday, February 12, 2018 - 1:46:31 PM
Last modification on : Friday, April 12, 2019 - 10:46:02 AM
Long-term archiving on : Monday, May 7, 2018 - 7:56:39 PM

File

preprint_mcom.pdf
Files produced by the author(s)

Identifiers

Citation

Hélène Barucq, Théophile Chaumont-Frelet, Christian Gout. Stability analysis of heterogeneous Helmholtz problems and finite element solution based on propagation media approximation. Mathematics of Computation, American Mathematical Society, 2017, 86 (307), pp.2129 - 2157. ⟨10.1090/mcom/3165⟩. ⟨hal-01408934⟩

Share

Metrics

Record views

399

Files downloads

374