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Cloaking via change of variables for the Helmholtz equation in the whole space

✍ Scribed by Hoai-Minh Nguyen

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
170 KB
Volume
63
Category
Article
ISSN
0010-3640

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## Abstract We show that the vorticity of a viscous flow in ℝ^3^ admits an atomic decomposition of the form __Ο‰__(__x, t__) = $ \textstyle \sum ^\infty \_{k = 1} $ __Ο‰~k~__(__x__ – __x~k~, t__), with localized and oscillating building blocks __Ο‰~k~__, if such a property is satisfied at the beginnin

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For high wave numbers, the Helmholtz equation su!ers the so-called &pollution e!ect'. This e!ect is directly related to the dispersion. A method to measure the dispersion on any numerical method related to the classical Galerkin FEM is presented. This method does not require to compute the numerical