Related papers: Numerical Relativity and Inhomogeneous Cosmologies
We review recent efforts to re-formulate the Einstein equations for fully relativistic numerical simulations. The so-called numerical relativity (computational simulations in general relativity) is a promising research field matching with…
This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…
We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view towards quantifying non-linear effects from cosmological inhomogeneities. We demonstrate fourth-order…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…
This thesis is concerned with formulations of the Einstein equations in axisymmetric spacetimes which are suitable for numerical evolutions. We develop two evolution systems based on the (2+1)+1 formalism. The first is a (partially)…
This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…
The application of numerical relativity to cosmological spacetimes is providing new insights into the behavior of Einstein's equations, beyond common approximations. In order for simulations to be performed as accurately and efficiently as…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve…
This thesis describes the application of numerical techniques to solve Einstein's field equations in three distinct cases. First we present the first long-term stable second order convergent Cauchy characteristic matching code in…
We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
In this paper we consider the single patch pseudo-spectral scheme for tensorial and spinorial evolution problems on the 2-sphere presented in [3,4] which is based on the spin-weighted spherical harmonics transform. We apply and extend this…
The effectiveness of the hyperbolic relaxation method for solving the Einstein constraint equations numerically is studied here on a variety of compact orientable three-manifolds. Convergent numerical solutions are found using this method…
In this work, we study of the algebraic-hyperbolic formulation of the Einstein constraint equations for numerically constructing initial data sets for inhomogeneous cosmological space-times with $\mathbb{T}^3$ topology. We implement a…
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…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
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…
One method for the numerical treatment of future null-infinity is to decouple coordinates from the tensor basis and choose each in a careful manner. This dual-frame approach is hampered by logarithmically divergent terms that appear in a…
Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…