Implicit-explicit evolution of single black holes

Journal Article · Sat Oct 15 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.84.084023· OSTI ID:21607907

Lau, Stephen R ^[1]; Lovelace, Geoffrey ^[2]; Pfeiffer, Harald P ^[3]

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1. Department of Mathematics and Statistics, The University of New Mexico, Albuquerque, New Mexico 87131 (United States)
2. Center for Radiophysics and Space Research, Cornell University, Ithaca, New York, 14853 (United States)
3. Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8 (Canada)

Numerical simulations of binary black holes - an important predictive tool for the detection of gravitational waves - are computationally expensive, especially for binaries with high mass ratios or with rapidly spinning constituent holes. Existing codes for evolving binary black holes rely on explicit time-stepping methods, for which the time-step size is limited by the smallest spatial scale through the Courant-Friedrichs-Lewy condition. Binary inspiral typically involves spatial scales (the spatial resolution required by a small or rapidly spinning hole) which are orders of magnitude smaller than the relevant (orbital, precession, and radiation-reaction) time scales characterizing the inspiral. Therefore, in explicit evolutions of binary black holes, the time-step size is typically orders of magnitude smaller than the relevant physical time scales. Implicit time-stepping methods allow for larger time steps, and they often reduce the total computational cost (without significant loss of accuracy) for problems dominated by spatial rather than temporal error, such as for binary-black-hole inspiral in corotating coordinates. However, fully implicit methods can be difficult to implement for nonlinear evolution systems like the Einstein equations. Therefore, in this paper we explore implicit-explicit (IMEX) methods and use them for the first time to evolve black-hole spacetimes. Specifically, as a first step toward IMEX evolution of a full binary-black-hole spacetime, we develop an IMEX algorithm for the generalized harmonic formulation of the Einstein equations and use this algorithm to evolve stationary and perturbed single-black-hole spacetimes. Numerical experiments explore the stability and computational efficiency of our method.

• OSTI ID: 21607907
• Journal Information: Physical Review. D, Particles Fields, Vol. 84, Issue 8; Other Information: DOI: 10.1103/PhysRevD.84.084023; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACCURACY
ALGORITHMS
BLACK HOLES
COMPUTERIZED SIMULATION
DETECTION
EFFICIENCY
EINSTEIN FIELD EQUATIONS
GRAVITATIONAL WAVE DETECTORS
GRAVITATIONAL WAVES
LOSSES
MASS
NONLINEAR PROBLEMS
PRECESSION
SPACE-TIME
SPATIAL RESOLUTION
STABILITY
EQUATIONS
FIELD EQUATIONS
MATHEMATICAL LOGIC
MEASURING INSTRUMENTS
RADIATION DETECTORS
RESOLUTION
SIMULATION