Related papers: Binary black hole simulation with an adaptive fini…
We present long term evolutions of a single black hole of mass $M$ with the BSSN system using pseudospectral methods. For our simulations we use the SGRID code where the BSSN system is implemented in its standard second order in space form.…
As a network of advanced-era gravitational wave detectors is nearing its design sensitivity, efficient and accurate waveform modeling becomes more and more relevant. Understanding of the nature of the signal being sought can have an order…
We present a new fully first order strongly hyperbolic representation of the BSSN formulation of Einstein's equations with optional constraint damping terms. We describe the characteristic fields of the system, discuss its hyperbolicity…
Approximate solutions to the Einstein field equations are a valuable tool to investigate gravitational phenomena. An important aspect of any approximation is to investigate and quantify its regime of validity. We present a study that…
We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…
We describe numerical techniques used in the construction of our 4th order evolution for the full Einstein equations, and assess the accuracy of representative solutions. The code is based on a null gauge with a quasi-spherical radial…
Numerical codes based on a direct implementation of the standard ADM formulation of Einstein's equations have generally failed to provide long-term stable and convergent evolutions of black hole spacetimes when excision is used to remove…
We describe a method for initializing characteristic evolutions of the Einstein equations using a linearized solution corresponding to purely outgoing radiation. This allows for a more consistent application of the characteristic (null…
New boundary conditions are constructed and tested numerically for a general first-order form of the Einstein evolution system. These conditions prevent constraint violations from entering the computational domain through timelike…
We experiment with several new modifications for the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein field equations and demonstrate how these modifications affect the stability of numerical black hole evolution…
We have recently constructed a numerical code that evolves a spherically symmetric spacetime using a hyperbolic formulation of Einstein's equations. For the case of a Schwarzschild black hole, this code works well at early times, but…
We construct a class of linear partial differential equations describing general perturbations of non-rotating black holes in 3D Cartesian coordinates. In contrast to the usual approach, a single equation treats all radiative $\ell -m$…
Combining deeper insight of Einstein's equations with sophisticated numerical techniques promises the ability to construct accurate numerical implementations of these equations. We illustrate this in two examples, the numerical evolution of…
In this paper we develop an $hp$-adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and…
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead…
A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the…
Construction of binary black hole initial data is a prerequisite for numerical evolutions of binary black holes. This paper reports improvements to the binary black hole initial data solver in the Spectral Einstein Code, to allow robust…
Numerical schemes for Einstein's vacuum equation are developed. Einstein's equation in harmonic gauge is second order symmetric hyperbolic. It is discretized in four-dimensional spacetime by Finite Differences, Finite Elements, and Interior…
Einstein's equations are known to lead to the formation of black holes and spacetime singularities. This appears to be a manifestation of the mathematical phenomenon of finite-time blowup: a formation of singularities from regular initial…
We present a new approach to the problem of binary black holes in the pre-coalescence stage, i.e. when the notion of orbit has still some meaning. Contrary to previous numerical treatments which are based on the initial value formulation of…