Hamiltonian relaxation

Marronetti, Pedro

doi:10.1088/0264-9381/22/12/009

Cited by 8 publications

(16 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, terms containing g ab ∂ jgab ≡ ∂ j lng are nominally zero becauseg = det(g ij ) = 1, but in practise we expect small violations in one of more of the constraints (19). Our result is consistent with recent work by Marronetti [11,12], where a constraint relaxation method is applied to the BSSN formulation. Although weak enforcement of the Hamiltonian constraint was found to provide significant improvement in the results [11], there was little change when a similar approach was applied to the momentum constraints [12].…”

Section: Discussionsupporting

confidence: 93%

“…Our result is consistent with recent work by Marronetti [11,12], where a constraint relaxation method is applied to the BSSN formulation. Although weak enforcement of the Hamiltonian constraint was found to provide significant improvement in the results [11], there was little change when a similar approach was applied to the momentum constraints [12]. As we have seen, the momentum constraints are already being directly enforced in the BSSN approach.…”

Section: Discussionsupporting

confidence: 93%

“…the first term of which is suggestive of the conformal connection coefficients defined by equation (11). The momentum constraints written in their most general form as evolution equations are then…”

Section: The Momentum Constraints As First-order Evolution Equationsmentioning

confidence: 99%

See 2 more Smart Citations

The BSSN Formulation Is a Partially Constrained Evolution System

Gentle

2010

Int. J. Mod. Phys. D

View full text Add to dashboard Cite

Abstract. Relativistic simulations in 3+1 dimensions typically monitor the Hamiltonian and momentum constraints during evolution, with significant violations of these constraints indicating the presence of instabilities. In this paper we rewrite the momentum constraints as first-order evolution equations, and show that the popular BSSN formulation of the Einstein equations explicitly uses the momentum constraints as evolution equations. We conjecture that this feature is a key reason for the relative success of the BSSN formulation in numerical relativity.

show abstract

Section: Discussionsupporting

confidence: 93%

Section: Discussionsupporting

confidence: 93%

See 1 more Smart Citation

The BSSN Formulation Is a Partially Constrained Evolution System

Gentle

2010

Int. J. Mod. Phys. D

View full text Add to dashboard Cite

show abstract

“…A similar approach has also been applied in numerical relativity via a Hamiltonian constraint relaxation method [23], which introduces a parabolic equation to approximately solve the Hamiltonian constraint. The parabolic equation is solved not in real (coordinate) time, but in some fiducial time until the Hamiltonian constraint has been relaxed.…”

Section: Introductionmentioning

confidence: 99%

“…It is here noted that hyperbolic and parabolic drivers have been constructed for the MHD equations, by introducing additional non-physical fields, whose time evolution drive the physical fields on the constraint surface, see for example [22] and references therein. A similar approach has also been applied in numerical relativity via a Hamiltonian constraint relaxation method [23], which introduces a parabolic equation to approximately solve the Hamiltonian constraint. The parabolic equation is solved not in real (coordinate) time, but in some fiducial time until the Hamiltonian constraint has been relaxed.…”

Section: Introductionmentioning

confidence: 99%

Mixed hyperbolic—second-order-parabolic formulations of general relativity

Paschalidis

2008

Phys. Rev. D

View full text Add to dashboard Cite

Two new formulations of general relativity are introduced. The first one is a parabolization of the Arnowitt, Deser, Misner (ADM) formulation and is derived by addition of combinations of the constraints and their derivatives to the right-hand-side of the ADM evolution equations. The desirable property of this modification is that it turns the surface of constraints into a local attractor because the constraint propagation equations become second-order parabolic independently of the gauge conditions employed. This system may be classified as mixed hyperbolic -second-order parabolic. The second formulation is a parabolization of the Kidder, Scheel, Teukolsky formulation and is a manifestly mixed strongly hyperbolic -second-order parabolic set of equations, bearing thus resemblance to the compressible Navier-Stokes equations. As a first test, a stability analysis of flat space is carried out and it is shown that the first modification exponentially damps and smoothes all constraint violating modes. These systems provide a new basis for constructing schemes for long-term and stable numerical integration of the Einstein field equations.

show abstract

Momentum constraint relaxation

Marronetti¹

2006

Class. Quantum Grav.

Self Cite

View full text Add to dashboard Cite

Full relativistic simulations in three dimensions invariably develop runaway modes that grow exponentially and are accompanied by violations of the Hamiltonian and momentum constraints. Recently, we introduced a numerical method (Hamiltonian relaxation) that greatly reduces the Hamiltonian constraint violation and helps improve the quality of the numerical model. We present here a method that controls the violation of the momentum constraint. The method is based on the addition of a longitudinal component to the traceless extrinsic curvature Ãij , generated by a vector potential w i , as outlined by York. The components of w i are relaxed to solve approximately the momentum constraint equations, pushing slowly the evolution toward the space of solutions of the constraint equations. We test this method with simulations of binary neutron stars in circular orbits and show that effectively controls the growth of the aforementioned violations. We also show that a full numerical enforcement of the constraints, as opposed to the gentle correction of the momentum relaxation scheme, results in the development of instabilities that stop the runs shortly.

show abstract

Hamiltonian relaxation

Cited by 8 publications

References 46 publications

The BSSN Formulation Is a Partially Constrained Evolution System

The BSSN Formulation Is a Partially Constrained Evolution System

Mixed hyperbolic—second-order-parabolic formulations of general relativity

Momentum constraint relaxation

Contact Info

Product

Resources

About