Controlling the Growth of Constraints in Hyperbolic Evolution Systems
arXiv:gr-qc/0402027 · doi:10.1103/PhysRevD.69.124025
Abstract
Motivated by the need to control the exponential growth of constraint violations in numerical solutions of the Einstein evolution equations, two methods are studied here for controlling this growth in general hyperbolic evolution systems. The first method adjusts the evolution equations dynamically, by adding multiples of the constraints, in a way designed to minimize this growth. The second method imposes special constraint preserving boundary conditions on the incoming components of the dynamical fields. The efficacy of these methods is tested by using them to control the growth of constraints in fully dynamical 3D numerical solutions of a particular representation of the Maxwell equations that is subject to constraint violations. The constraint preserving boundary conditions are found to be much more effective than active constraint control in the case of this Maxwell system.
arXiv commentfinal version to be published in Physical Review D
References in corpus (17)
- Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations
- Well-Posed Initial-Boundary Evolution in General Relativity
- Black hole evolution by spectral methods
- Einstein's Equations with Asymptotically Stable Constraint Propagation
- Critical Collapse of the Massless Scalar Field in Axisymmetry
- Well posed constraint-preserving boundary conditions for the linearized Einstein equations
- Boundary conditions in linearized harmonic gravity
- Constraint-preserving boundary conditions in numerical relativity
- An Axisymmetric Gravitational Collapse Code
- 3D simulations of linearized scalar fields in Kerr spacetime
- Toward stable 3D numerical evolutions of black-hole spacetimes
- Einstein boundary conditions for the 3+1 Einstein equations
- Boundary conditions for hyperbolic formulations of the Einstein equations
- Detecting ill posed boundary conditions in General Relativity
- Energy Norms and the Stability of the Einstein Evolution Equations
- Hyperbolic formulations and numerical relativity II: Asymptotically constrained systems of the Einstein equations
- On the Effect of Constraint Enforcement on the Quality of Numerical Solutions in General Relativity
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- Numerical Relativity Using a Generalized Harmonic Decomposition
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- An Introduction to Well-posedness and Free-evolution
- Optimal Constraint Projection for Hyperbolic Evolution Systems
- Comparison of high-accuracy numerical simulations of black-hole binaries with stationary phase post-Newtonian template waveforms for Initial and Advanced LIGO
- Symmetric hyperbolic form of systems of second-order evolution equations subject to constraints
- The Midpoint Rule as a Variational--Symplectic Integrator. I. Hamiltonian Systems
- A model problem for the initial-boundary value formulation of Einstein's field equations
- Rotating star initial data for a constrained scheme in numerical relativity
- Absorbing boundary conditions for Einstein's field equations
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- Numerical solutions of Einstein's equations for cosmological spacetimes with spatial topology S3 and symmetry group U(1)
- Schwarzschild Tests of the Wahlquist-Estabrook-Buchman-Bardeen Tetrad Formulation for Numerical Relativity
- The Dynamics of Inhomogeneous Cosmologies
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- Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations
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- Modifying the Einstein Equations off the Constraint Hypersuface