Numerical stability of the AA evolution system compared to the ADM and BSSN systems
arXiv:gr-qc/0310100 · doi:10.1103/PhysRevD.74.084022
Abstract
We explore the numerical stability properties of an evolution system suggested by Alekseenko and Arnold. We examine its behavior on a set of standardized testbeds, and we evolve a single black hole with different gauges. Based on a comparison with two other evolution systems with well-known properties, we discuss some of the strengths and limitations of such simple tests in predicting numerical stability in general.
16 pages, 12 figures
References in corpus (28)
- On the Numerical Integration of Einstein's Field Equations
- Gauge conditions for long-term numerical black hole evolutions without excision
- A simple construction of initial data for multiple black holes
- Numerical simulation of orbiting black holes
- Modeling gravitational radiation from coalescing binary black holes
- Symmetry without Symmetry: Numerical Simulation of Axisymmetric Systems using Cartesian Grids
- Simple excision of a black hole in 3+1 numerical relativity
- Three dimensional numerical relativity: the evolution of black holes
- Toward standard testbeds for numerical relativity
- Binary Black Hole Mergers in 3d Numerical Relativity
- Grazing Collisions of Black Holes via the Excision of Singularities
- Plunge waveforms from inspiralling binary black holes
- Towards an understanding of the stability properties of the 3+1 evolution equations in general relativity
- A symmetry-breaking mechanism for the Z4 general-covariant evolution system
- Hydrodynamic Simulations in 3+1 General Relativity
- Hyperbolicity of the BSSN system of Einstein evolution equations
- The 3D Grazing Collision of Two Black Holes
- Gravitational waves from black hole collisions via an eclectic approach
- Symmetric hyperbolicity and consistent boundary conditions for second-order Einstein equations
- Adaptive mesh and geodesically sliced Schwarzschild spacetime in 3+1 dimensions
- The coalescence remnant of spinning binary black holes
- Well-posed forms of the 3+1 conformally-decomposed Einstein equations
- Symmetric hyperbolic form of systems of second-order evolution equations subject to constraints
- Convergence and stability in numerical relativity
- A Conformal Hyperbolic Formulation of the Einstein Equations
- Illustrating Stability Properties of Numerical Relativity in Electrodynamics
- Energy Norms and the Stability of the Einstein Evolution Equations
- New first-order formulation for the Einstein equations
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- Binary black holes on a budget: Simulations using workstations
- Testing the Accuracy and Stability of Spectral Methods in Numerical Relativity
- Long term black hole evolution with the BSSN system by pseudospectral methods
- Towards a gauge-polyvalent Numerical Relativity code
- A spectral method algorithm for numerical simulations of gravitational fields
- Numerical performance of the parabolized ADM (PADM) formulation of General Relativity
- Numerical experiments of adjusted BSSN systems for controlling constraint violations
- Aliasing Instabilities in the Numerical Evolution of the Einstein Field Equations