Calculating initial data for the conformal Einstein equations by pseudo-spectral methods

Journal of Computational and Applied Mathematics

Volumn 109, Issue 1-2, 1999, Pages 475-491

  Frauendiener, Jörg ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

Conformal constraints; Initial data; Numerical relativity; Yamabe equation* Pseudo spectral methods

Indexed keywords

COMPUTATIONAL GEOMETRY; CONSTRAINT THEORY; DATA STRUCTURES; ITERATIVE METHODS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; PROBLEM SOLVING;

CONFORMAL EINSTEIN EQUATIONS; NUMERICAL RELATIVITY; PSEUDO-SPECTRAL METHODS; YAMABE EQUATION;

SPECTRUM ANALYSIS;

EID: 0032594787     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00168-5     Document Type: Article

References (26)

1. Andersson L., Chruściel P.T. On hyperboloidal Cauchy data for vacuum Einstein equations and obstructions to smoothness of scri. Comm. Math. Phys. 149:1994;587-612.
2. L. Andersson, P.T. Chruściel, H. Friedrich, On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein's field equations, Comm. Math. Phys. 149 (1992) 587-612.
3. S. Bonazzola, E. Gourgoulhon, J.-A. Marck, Spectral methods in general relativistic astrophysics, this volume, J. Comp. Appl. Math. 109 (1999) 433.
4. C. Canuto, M.Y. Houssaini, A. Quarteroni, T.A. Zang, Spectral Methods in Fluid Dynamics, Springer, Berlin, 1988.
5. B. Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge University Press, Cambridge, 1996.
6. J. Frauendiener, Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. I. The conformal field equations, Phys. Rev. D. 58 (1998).
7. J. Frauendiener, Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. II. The evolution equations, Phys. Rev. D. 58 (1998).
8. Friedrich H. The asymptotic characteristic initial value problem for Einstein's vacuum field equations as an initial value problem for a first-order quasilinear symmetric hyperbolic system. Proc. Roy. Soc. London A. 378:1981;401-421.
9. H. Friedrich, Cauchy problems for the conformal vacuum field equations in general relativity, Comm. Math. Phys. 91 (1983) 445-472.
10. H. Friedrich, On hyperboloidal hypersurfaces, in: R. d'Inverno (Ed.), Approaches to Numerical Relativity, Cambridge University Press, Cambridge, 1993.
11. H. Friedrich, private communication.
12. G.H. Golub, C.F. van Loan, Matrix Computations, The Johns Hopkins University Press, Baltimore, 1989.
13. D. Gottlieb, S.A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM-CBMS, Philadelphia, 1977.
14. P. Hübner, Black hole spacetimes on grids with trivial boundaries, preprint AEI-062,gr-qc/9804065.
15. Hübner P. General relativistic scalar field models and asymptotic flatness. Class. Quant. Grav. 12:1995;791-808.
16. P. Hübner, private communication.
17. J. Isenberg, J. Park, Asymptotically hyberbolic nonconstant mean curvature solutions of the Einstein constraint equations, Class. Quant. Grav. 14 (1997) A189-A201.
18. Kánnár J. Hyperboloidal initial data for the vacuum Einstein equations with cosmological constant. Class. Quant. Grav. 13:1996;3075-3084.
19. C.T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia, 1995.
20. Kreiss H.-O., Oliger J. Comparison of accurate methods for the integration of hyperbolic equations. Tellus. 24:1972;199-215.
21. Orszag S.A. Spectral Methods for Problems in Complex Geometries. J. Comput. Phys. 37:1980;70-92.
22. Penrose R. A generalized inverse for matrices. Proc. Camb. Philos. Soc. 51:1955;406-413.
23. Schmidt B.G. Vacuum space-times with toroidal null infinities. Class. Quant. Grav. 13:1996;2811-2816.
24. T. Skalický, Laspack reference manual. http://www.tu-dresden.de/mwism/skalicky/laspack/laspack.html, Dresden University of Technology, 1996.
25. J. Stoer, R. Bulirsch, Einführung in die Numerische Mathematik II, Springer, Berlin, 1978.
26. L.N. Trefethen, D. Bau, Numerical Linear Algebra, SIAM, Philadelphia, 1997.