Related papers: Initial Conditions for Numerical Relativity -- Int…
In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several…
Gravitational waves radiated during binary black hole coalescence is a perfect probe for studying the characteristics of strong gravity. Advanced techniques for creating numerical relativity substitute models for eccentric binary black hole…
Numerical relativity has brought about profound and wide-ranging influences on modern astrophysics and gravitational-wave astronomy. In this study, we present a user-friendly Python interface for the numerical relativity code AMSS-NCKU.…
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…
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:…
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…
This thesis details an effort to generate astrophysically interesting solutions to the two-body problem in General Relativity. The thesis consists of two main parts. The first part presents an analytical variational principle for describing…
According to the theory of general relativity, the relative acceleration of masses generates gravitational radiation. Although gravitational radiation has not yet been detected, it is believed that extremely violent cosmic events, such as…
This work is concerned with the quantification of the epistemic uncertainties induced the discretization of partial differential equations. Following the paradigm of probabilistic numerics, we quantify this uncertainty probabilistically.…
In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton method and an adaptive…
Discontinuous Galerkin (DG) methods for solving elliptic equations are gaining popularity in the computational physics community for their high-order spectral convergence and their potential for parallelization on computing clusters.…
In this paper a new double-domain spectral method to compute binary black hole excision initial data is presented. The method solves a system of elliptic partial differential equations in the exterior of two excised spheres. At the surface…
This work concerns with the existence of solutions for the following class of nonlocal elliptic problems \begin{eqnarray}\label{eq:0.1} &&\left\{\begin{array}{l} (-\Delta)^{s} u+u=|u|^{p-2} u \text { in } \Omega_{r} \\ u \geq 0 \quad \text…
GRTresna is a multigrid solver designed to solve the constraint equations for the initial data required in numerical relativity simulations. In particular, it is focussed on scenarios with fundamental fields around black holes and…
This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately,…
In this article we show the crucial role of elliptic regularity theory for the development of efficient numerical methods for the solution of some variational problems. Here we focus to a class of elliptic multiobjective optimal control…
Tremendous progress has been made towards the solution of the binary-black-hole problem in numerical relativity. The waveforms produced by numerical relativity will play a role in gravitational wave detection as either test-beds for…
Numerical Relativity is a mature field with many applications in Astrophysics, Cosmology and even in Fundamental Physics. As such, we are entering a stage in which new sophisticated methods adapted to open problems are being developed. In…
It is well known that multigrid methods are optimally efficient for solution of elliptic equations (O(N)), which means that effort is proportional to the number of points at which the solution is evaluated). Thus this is an ideal method to…
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 $\ell -m$…