Numerical Evolution of axisymmetric vacuum spacetimes: a code based on the Galerkin method

Abstract

We present the first numerical code based on the Galerkin and Collocation methods to integrate the field equations of the Bondi problem. The Galerkin method like all spectral methods provide high accuracy with moderate computational effort. Several numerical tests were performed to verify the issues of convergence, stability and accuracy with promising results. This code opens up several possibilities of applications in more general scenarios for studying the evolution of spacetimes with gravitational waves.

11 pages, 6 figures. To appear in Classical and Quantum Gravity

References in corpus (3)

• Spectral Methods for Numerical Relativity
• Characteristic Evolution and Matching
• A framework for large-scale relativistic simulations in the characteristic approach

Cited by in corpus (10)

• Spectral Characteristic Evolution: A New Algorithm for Gravitational Wave Propagation
• The affine-null formulation of the gravitational equations: spherical case
• Extended two-dimensional characteristic framework to study nonrotating black holes
• Puncture black hole initial data: a single domain Galerkin-Collocation method for trumpet and wormhole data sets
• Galerkin-Collocation domain decomposition method for arbitrary binary black holes
• The Bondi problem revisited: a spectral domain decomposition code
• Three dimensional distorted black holes: using the Galerkin-Collocation method
• Point Particle Binary System with Components of Different Masses in the Linear Regime of the Characteristic Formulation of General Relativity
• New numerical framework for the generalized Baumgarte-Shapiro-Shibata-Nakamura formulation: The vacuum case for spherical symmetry
• On the Linear Regime of the Characteristic formulation of General relativity in the Minkowski and Schwarzschild's Backgrounds