Related papers: The Hyperboloidal Numerical Evolution of a Good-Ba…
The Good-Bad-Ugly-F model is a system of semi-linear wave equations that mimics the asymptotic form of the Einstein field equations in generalized harmonic gauge with specific constraint damping and suitable gauge source functions. These…
All strategies for the treatment of future null-infinity in numerical relativity involve some form of regularization of the field equations. In a recent proposal that relies on the dual foliation formalism this is achieved by the use of an…
A heuristic method to find asymptotic solutions to a system of non-linear wave equations near null infinity is proposed. The non-linearities in this model, dubbed good-bad-ugly, are known to mimic the ones present in the Einstein field…
Upcoming gravitational wave-experiments promise a window for discovering new physics in astronomy. Detection sensitivity of the broadband laser interferometric detectors LIGO/VIRGO may be enhanced by matched filtering with accurate…
We employ an adapted version of H\"ormander's asymptotic systems method to show heuristically that the standard good-bad-ugly model admits formal polyhomogeneous asymptotic solutions near null infinity. In a related earlier approach, our…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
A long-standing problem in numerical relativity is the satisfactory treatment of future null-infinity. We propose an approach for the evolution of hyperboloidal initial data in which the outer boundary of the computational domain is placed…
We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on…
We consider the hyperboloidal initial value problem in numerical relativity, motivated by the goal to evolve radiating compact objects such as black hole binaries with a numerical grid that includes null infinity. Unconstrained evolution…
The dual-frame formalism leads to an approach to extend numerical relativity simulations in generalized harmonic gauge (GHG) all the way to null infinity. A major setback is that without care, even simple choices of initial data give rise…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
We consider an approach to the hyperboloidal evolution problem based on the Einstein equations written for a rescaled metric. It is shown that a conformal scale factor can be freely prescribed a priori in terms of coordinates in a…
We address the hyperboloidal initial value problem in the context of Numerical Relativity, motivated by its evolution on hyperboloidal slices: smooth spacelike slices that reach future null infinity, the "location" in spacetime where…
Numerical relativity describes a discrete initial value problem for general relativity. A choice of gauge involves slicing space-time into space-like hypersurfaces. This introduces past and future gauge relative to the hypersurface of…
We report on the successful numerical evolution of the compactified hyperboloidal initial value problem in general relativity using generalized harmonic gauge. We work in spherical symmetry, using a massless scalar field to drive dynamics.…
This is the second in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper the numerical methods used to solve the system of evolution…
The hyperboloidal initial value problem is addressed in the context of Numerical Relativity, motivated by its use of hyperboloidal slices - smooth spacelike slices that reach future null infinity, the "place" in spacetime where radiation is…
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems.…
We present the first stable dynamical numerical evolutions of the Einstein equations in terms of a conformally rescaled metric on hyperboloidal hypersurfaces extending to future null infinity. Axisymmetry is imposed in order to reduce the…
The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the…