Solving the Einstein constraints in periodic spaces with a multigrid approach

Abstract

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.

25 pages, 15 figures. Fixed typos, added references and software release information

References in corpus (5)

• Spikes in the Mixmaster regime of G_2 cosmologies
• Conformal Thin-Sandwich Solver for Generic Initial Data
• Evolution of a family of expanding cubic black-hole lattices in numerical relativity
• The constraint equations for the Einstein-scalar field system on compact manifolds
• A weak acceleration effect due to residual gravity in a multiply connected universe

Cited by in corpus (22)

• Effects of nonlinear inhomogeneity on the cosmic expansion with numerical relativity
• The Effects of Potential Shape on Inhomogeneous Inflation
• Black Hole Universe with $\Lambda$
• Primordial black hole formation with full numerical relativity
• Parameterized Post-Newtonian Cosmology
• Post-Newtonian Cosmological Modelling
• CTTK: A new method to solve the initial data constraints in numerical relativity
• Persistent Black Holes in Bouncing Cosmologies
• Light propagation through black-hole lattices
• Black-Hole Lattices as Cosmological Models
• Ray tracing and Hubble diagrams in post-Newtonian cosmology
• Cosmological backreaction in the presence of radiation and a cosmological constant
• An automatically generated code for relativistic inhomogeneous cosmologies
• Exact Initial Data for Black Hole Universes with a Cosmological Constant
• Gravitational Collapse of a Massless Scalar Field in a Periodic Box
• Cosmology using numerical relativity
• Solving the initial conditions problem for modified gravity theories
• Cosmic backreaction and Gauss's law
• The Method of Images in Cosmology
• Cosmological Solutions with Charged Black Holes
• Constant-mean-curvature Slicing of the Swiss-cheese Universe
• A Gravitational Wave Background from Primordial Black Hole Lattices in Matter Dominated Era