1302.6537 (Agnès Bachelot-Motet)

Wave computation on the Poincaré dodecahedral space    [PDF]

Agnès Bachelot-Motet

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 in 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.

View original: http://arxiv.org/abs/1302.6537