International Journal of Theoretical Physics

, Volume 36, Issue 4, pp 815–839 | Cite as

Parallelizable implicit evolution scheme for Regge calculus

  • John W. Barrett
  • Mark Galassi
  • Warner A. Miller
  • Rafael D. Sorkin
  • Philip A. Tuckey
  • Ruth M. Williams
Article

Abstract

The role of Regge calculus as a tool for numerical relativity is discussed, and a parallelizable implicit evolution scheme described. Because of the structure of the Regge equations, it is possible to advance the vertices of a triangulated spacelike hypersurface in isolation, solving at each vertex a purely local system of implicit equations for the new edge lengths involved. (In particular, equations of global “elliptic type” do not arise.) Consequently, there exists a parallel evolution scheme which divides the vertices into families of nonadjacent elements and advances all the vertices of a family simultaneously. The relation between the structure of the equations of motion and the Bianchi identities is also considered. The method is illustrated by a preliminary application to a 600-cell Friedmann cosmology. The parallelizable evolution algorithm described in this paper should enable Regge calculus to be a viable discretization technique in numerical relativity.

Keywords

Quantum Gravity Edge Length Bianchi Identity Vertical Edge Spacelike Hypersurface 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • John W. Barrett
    • 1
  • Mark Galassi
    • 2
  • Warner A. Miller
    • 3
  • Rafael D. Sorkin
    • 4
    • 5
  • Philip A. Tuckey
    • 6
  • Ruth M. Williams
    • 7
  1. 1.Mathematics DepartmentUniversity of NottinghamNottinghamUK
  2. 2.Space Data Systems GroupLos Alamos National LaboratoryLos Alamos
  3. 3.Theoretical DivisionLos Alamos National LaboratoryLos Alamos
  4. 4.Physics DepartmentSyracuse UniversitySyracuse
  5. 5.Departamento de Gravitacion y Teoria de Campos, Instituto de Ciencias NuclearesUNAMMexicoMexico
  6. 6.Laboratoire de Physique MoléculaireUniversité de Franche-ComtéBesançonFrance
  7. 7.DAMTPCambridgeUK

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