Physics
Scientific paper
Jan 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phdt........59g&link_type=abstract
Thesis (PH.D.)--STATE UNIVERSITY OF NEW YORK AT STONY BROOK, 1992.Source: Dissertation Abstracts International, Volume: 54-02,
Physics
2
Regge Calculus, Numerical Relativity
Scientific paper
I present the results of my work aimed at making Regge Calculus a practical tool for numerical relativity. The principal results are a formalism for solving the Regge equations in the general case, a working software package r3+1 which implements these methods, and a collection of numerical results produced by this software. The formalism for solving the Regge equations consists of a set of algorithms for constructing and analyzing arbitrary simplicial lattices, calculating deficit angles, and (for the first time) calculating the Jacobian of the Regge equations. I also present a definition of lapse and shift in Regge Calculus. At this time the software package consists of approximately ten thousand lines of C++ code which offer a user interface, lattice analysis routines, and routines to calculate and solve the Regge equations with arbitrary choice lapse and shift. The Regge equations are solved using Newton's method and conjugate gradient methods. The numerical runs presented here (1) confirm the validity of the methods used; (2) examine the structure of diffeomorphism freedom in Regge Calculus, giving the first verification that one can choose lapse and shift freely; (3) examine the Bianchi identities and quantify the extent to which time evolution in Regge Calculus preserves constraints, finding that the constraints are proportional to the third power of the lattice spacing.
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