Solving the Einstein constraints in periodic spaces with a multigrid approach

Understand

Novel applications of Numerical Relativity demand for more flexible algorithms and tools.

• In this paper, I develop and test a multigrid solver, based on the infrastructure provided by the Einstein Toolkit, for elliptic partial differential equations on spaces with periodic boundary conditions.
• This type of boundary often characterizes the numerical representation of cosmological models, where space is assumed to be made up of identical copies of a single fiducial domain, so that only a finite volume (with periodic boundary conditions at its edges) needs to be simulated.
• After a few tests and comparisons with existing codes, I use the solver to generate initial data for an infinite, periodic, cubic black-hole lattice.