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Solving the Einstein constraints in periodic spaces with a multigrid approach. (English) Zbl 1470.83007

Summary: Novel applications of Numerical Relativity demand 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 (PBCs). 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 PBCs 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.

MSC:

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C15 Exact solutions to problems in general relativity and gravitational theory
83-08 Computational methods for problems pertaining to relativity and gravitational theory
83C57 Black holes
83C27 Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory
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