Adrian P Gentle et al 2004 Class. Quantum Grav. 21 83 doi:10.1088/0264-9381/21/1/006
Adrian P Gentle1,2, Nathan D George1,3, Arkady Kheyfets1,4 and Warner A Miller1,5
Show affiliationsThe Einstein equations have proved surprisingly difficult to solve numerically. A standard diagnostic of the problems which plague the field is the failure of computational schemes to satisfy the constraints, which are known to be mathematically conserved by the evolution equations. We describe a new approach to rewriting the constraints as first-order evolution equations, thereby guaranteeing that they are satisfied to a chosen accuracy by any discretization scheme. This introduces a set of four subsidiary constraints which are far simpler than the standard constraint equations and which should be more easily conserved in computational applications. We explore the manner in which the momentum constraints are already incorporated in several existing formulations of the Einstein equations, and demonstrate the ease with which our new constraint-conserving approach can be incorporated into these schemes.
70H45 Constrained dynamics, Dirac's theory of constraints (See also 70F20, 70F25, 70Gxx)
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 1 (7 January 2004)
Received 1 July 2003
Published 20 November 2003
Adrian P Gentle et al 2004 Class. Quantum Grav. 21 83
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