Solving the Einstein constraints in periodic spaces with a multigrid approach

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). Th...

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Bibliographic Details
Published in:Classical and quantum gravity 2014-02, Vol.31 (3), p.35004
Main Author: Bentivegna, Eloisa
Format: Article
Language:English
Subjects:
Algorithms
Astronomical models
Computer simulation
Demand
initial data
numerical relativity
Quantum gravity
Reproduction
Solvers
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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.
ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/31/3/035004