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NUMERICAL METHODS FOR THE EINSTEIN EQUATIONS IN NULL QUASI-SPHERICAL COORDINATES.
- Source :
- SIAM Journal on Scientific Computing; 2000, Vol. 22 Issue 3, p917-950, 34p
- Publication Year :
- 2000
-
Abstract
- We describe algorithms used in our construction of a fourth-order in time evolution for the full Einstein equations and assess the accuracy of some representative solutions. The scheme employs several novel geometric and numerical techniques, including a geometrically invariant co- ordinate gauge, which leads to a characteristic-transport formulation of the underlying hyperbolic system, combined with a ‘method of lines’ evolution; convolution splines for radial interpolation, regridding, differentiation, and noise suppression; representations using spin-weighted spherical har- monics; and a spectral preconditioner for solving a class of first-order elliptic systems on S<superscript>2</superscript>. Initial data for the evolution is unconstrained, subject only to a mild size condition. For sample initial data of ‘intermediate’ strength (19% of the total mass in gravitational energy), the code is accurate to 1 part in 105, until null time z = 55m when the coordinate condition breaks down. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10648275
- Volume :
- 22
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Scientific Computing
- Publication Type :
- Academic Journal
- Accession number :
- 13205028
- Full Text :
- https://doi.org/10.1137/S1064827599356171