Wave computation on the Poincaré dodecahedral space

Abstract

We compute the waves propagating on a compact 3-manifold of constant positive curvature with a non trivial topology: the Poincaré 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.

31 pages, 8 figures

References in corpus (4)

• Lagrangian theory of structure formation in relativistic cosmology II: average properties of a generic evolution model
• A smooth introduction to the wavefront set
• A new analysis of Poincaré dodecahedral space model
• The Shape and Topology of the Universe

Cited by in corpus (1)

• Waves on accelerating dodecahedral universes