Multigrid elliptic equation solver with adaptive mesh refinement

Brown, J. David; Lowe, Lisa L.

doi:10.1016/j.jcp.2005.03.026

Cited by 34 publications

(39 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This approach is used to construct the majority of black-hole-binary initial data used in current numerical simulations, and the elliptic solve is performed either with mesh-refinement finite-difference solvers [22] or, in most cases, by an elegant single-domain spectral approach [23], which we will adopt for the work presented here.…”

Section: Background: a Brief Summary Of Wormholes Trumpets And Pmentioning

confidence: 99%

“…The conformal-factor ansatz is now provided by replacing the ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 3M=2r p term in (13) with DðÞ= ffiffi ffi r p . In the numerical procedure to solve the Hamiltonian constraint, the derivatives of DðÞ required in the construction ofr 2 c s are trivial to calculate in our Mathematica-based solver, because DðÞ is available from the solution to (22) …”

Section: B Solution Of the Nonlinear Angular-dependence Odementioning

confidence: 99%

See 1 more Smart Citation

Bowen-York trumpet data and black-hole simulations

2009

View full text Add to dashboard Cite

Type of publicationArticle (peer-reviewed) The most popular method to construct initial data for black-hole-binary simulations is the puncture method, in which compactified wormholes are given linear and angular momentum via the Bowen-York extrinsic curvature. When these data are evolved, they quickly approach a trumpet topology, suggesting that it would be preferable to use data that are in trumpet form from the outset. To achieve this, we extend the puncture method to allow the construction of Bowen-York trumpets, including an outline of an existence and uniqueness proof of the solutions. We construct boosted, spinning and binary Bowen-York puncture trumpets using a single-domain pseudospectral elliptic solver, and evolve the binary data and compare with standard wormhole-data results. We also show that for boosted trumpets the black-hole mass can be prescribed a priori, without recourse to the iterative procedure that is necessary for wormhole data.

show abstract

Section: Background: a Brief Summary Of Wormholes Trumpets And Pmentioning

confidence: 99%

Section: B Solution Of the Nonlinear Angular-dependence Odementioning

confidence: 99%

Bowen-York trumpet data and black-hole simulations

2009

View full text Add to dashboard Cite

show abstract

“…We will use as a test case a single black hole, given by Bowen-York puncture initial data [12] (as computed by the elliptic solver AMRMG [13]), with unit puncture mass and momentum such that its physical speed should be half the speed of light. We evolve this data with our Hahndol code [9], which uses the usual, conformal BSSN formulation of Einstein's evolution equations on a cellcentered numerical grid, with 4 th -order spatial differencing and 4 th -order Runge-Kutta time-integration.…”

Section: Original 1+log Slicing and Gamma-driver Shift Conditionsmentioning

confidence: 99%

How to move a black hole without excision: Gauge conditions for the numerical evolution of a moving puncture

et al. 2006

View full text Add to dashboard Cite

Recent demonstrations of unexcised black holes traversing across computational grids represent a significant advance in numerical relativity. Stable and accurate simulations of multiple orbits, and their radiated waves, result. This capability is critically undergirded by a careful choice of gauge. Here we present analytic considerations which suggest certain gauge choices, and numerically demonstrate their efficacy in evolving a single moving puncture black hole.

show abstract

“…The nonsingular function u is calculated by solving the Hamiltonian constraint equation using the second-order-convergent elliptic solver AMRMG [49].…”

Section: Initial Datamentioning

confidence: 99%

Recoiling from a kick in the head-on collision of spinning black holes

et al. 2007

View full text Add to dashboard Cite

Recoil "kicks" induced by gravitational radiation are expected in the inspiral and merger of black holes. Recently the numerical relativity community has begun to measure the significant kicks found when both unequal masses and spins are considered. Because understanding the cause and magnitude of each component of this kick may be complicated in inspiral simulations, we consider these effects in the context of a simple test problem. We study recoils from collisions of binaries with initially head-on trajectories, starting with the simplest case of equal masses with no spin and then adding spin and varying the mass ratio, both separately and jointly. We find spininduced recoils to be significant relative to unequal-mass recoils even in head-on configurations.Additionally, it appears that the scaling of transverse kicks with spins is consistent with postNewtonian theory, even though the kick is generated in the nonlinear merger interaction, where post-Newtonian theory should not apply. This suggests that a simple heuristic description might be effective in the estimation of spin-kicks.

show abstract

Multigrid elliptic equation solver with adaptive mesh refinement

Cited by 34 publications

References 26 publications

Bowen-York trumpet data and black-hole simulations

Bowen-York trumpet data and black-hole simulations

How to move a black hole without excision: Gauge conditions for the numerical evolution of a moving puncture

Recoiling from a kick in the head-on collision of spinning black holes

Contact Info

Product

Resources

About