WAVE COMPUTATION ON THE HYPERBOLIC DOUBLE DOUGHNUT
Author(s): Agnes Bachelot-Motet Universite de Bordeaux, Institut de Mathematiques, UMR CNRS 5251, F-33405 Talence Cedex
Pages: 790-806
Year: 2010 Issue: 6
Journal: Journal of Computational Mathematics
Keyword: Wave equation; Hyperbolic manifold; Finite elements; Quantum chaos;
Abstract: <正> We compute the waves propagating on the compact surface of constant negative curvatureand genus 2 that is a toy model in quantum chaos theory and cosmic topology.Weadopt a variational approach using finite elements.We have to implement the action of thefuchsian group by suitable boundary conditions of periodic type.Despite the ergodicity ofthe dynamics that is quantum weak mixing,the computation is very accurate.A spectralanalysis of the transient waves allows to compute the spectrum and the eigenfunctions ofthe Laplace-Beltrami operator.We test the exponential decay due to a localized dumpingsatisfying the assumption of geometric control.
Pages: 790-806
Year: 2010 Issue: 6
Journal: Journal of Computational Mathematics
Keyword: Wave equation; Hyperbolic manifold; Finite elements; Quantum chaos;
Abstract: <正> We compute the waves propagating on the compact surface of constant negative curvatureand genus 2 that is a toy model in quantum chaos theory and cosmic topology.Weadopt a variational approach using finite elements.We have to implement the action of thefuchsian group by suitable boundary conditions of periodic type.Despite the ergodicity ofthe dynamics that is quantum weak mixing,the computation is very accurate.A spectralanalysis of the transient waves allows to compute the spectrum and the eigenfunctions ofthe Laplace-Beltrami operator.We test the exponential decay due to a localized dumpingsatisfying the assumption of geometric control.
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