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arXiv · 1302.6537

Wave computation on the Poincar\'e dodecahedral space

Agnès Bachelot-Motet
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Abstract

We compute the waves propagating on a compact 3-manifold of constant positive curvature with a non trivial topology: the Poincar\'e dodecahedral space that is a plausible model of multi-connected universe. We transform the Cauchy problem to a mixed problem posed on a fundamental domain determined by the quaternionic calculus. We adopt a variational approach using a space of finite elements that is invariant under the action of the binary icosahedral group. The computation of the transient waves is validated with their spectral analysis by computing a lot of eigenvalues of the Laplace-Beltrami operator.

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Agnès Bachelot-Motet. 2013-02-26. Wave computation on the Poincar\'e dodecahedral space. https://doi.org/10.1088/0264-9381%2F30%2F23%2F235010

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