Gioel Calabrese et al 2004 Class. Quantum Grav. 21 5735 doi:10.1088/0264-9381/21/24/004
Gioel Calabrese1,2, Luis Lehner1, Oscar Reula3, Olivier Sarbach1 and Manuel Tiglio1,4,5
Show affiliationsWe discuss finite difference techniques for hyperbolic equations in non-trivial domains, as those that arise when simulating black-hole spacetimes. In particular, we construct dissipative and difference operators that satisfy the summation by parts property in domains with excised multiple cubic regions. This property can be used to derive semi-discrete energy estimates for the associated initial-boundary value problem which in turn can be used to prove numerical stability.
02.60.Lj Ordinary and partial differential equations; boundary value problems
04.25.-g Approximation methods; equations of motion
47B39 Difference operators (See also 39A70)
65M06 Finite difference methods
Issue 24 (21 December 2004)
Received 29 July 2004, in final form 8 October 2004
Published 22 November 2004
Gioel Calabrese et al 2004 Class. Quantum Grav. 21 5735
Teng Hao et al 2009 Chinese Phys. Lett. 26 113201
Itzhak Bars 2001 Class. Quantum Grav. 18 3113
Subhanjoy Mohanty et al. 2005 ApJ 626 498
P Mason et al 2005 J. Phys. G: Nucl. Part. Phys. 31 S1729
K. L. Luhman et al 2005 ApJ 635 L93
Kazuya Saigo and Kohji Tomisaka 2006 ApJ 645 381
G S Bisnovatyi-Kogan and V N Rudenko 2004 Class. Quantum Grav. 21 3347
Yusaku Fujii and Kazuhito Shimada 2006 Meas. Sci. Technol. 17 2705
R Bruzzese et al 1988 J. Phys. D: Appl. Phys. 21 1710