Wave Computation on the Hyperbolic Double Doughnut

Details Wave Computation on the Hyperbolic Double Doughnut Wave Computation on the Hyperbolic Double Doughnut

2009-02-07

arxiv.org/abs/0902.1249v1

J. Comp. Math., 28 (2010), pp. 790-806

Mathematics

Numerical Analysis

13 pages, 6 figures

Scientific paper

We compute the waves propagating on the compact surface of constant negative curvature and genus 2. We adopt a variational approach using finite elements. We have to implement the action of the fuchsian group by suitable boundary conditions of periodic type. A spectral analysis of the wave allows to compute the first eigenvalues of the Laplace-Beltrami operator. We test the exponential decay due to a localized dumping and the ergodicity of the geodesic flow.

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