Related papers: Initial Conditions for Numerical Relativity -- Int…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
We present a method for computing the evolution of a spacetime containing a massive particle and a black hole. The essential idea is that the gravitational field is evolved using full numerical relativity, with the particle generating a…
We review recent progress in the application of numerical relativity techniques to astrophysics and high-energy physics. We focus on some developments that took place within the "Numerical Relativity and High Energy Physics" network, a…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
The nonlinear behavior of higher dimensional black hole spacetimes is of interest in several contexts, ranging from an understanding of cosmic censorship to black hole production in high-energy collisions. However, nonlinear numerical…
This paper presents a quasi-local method of studying the physics of dynamical black holes in numerical simulations. This is done within the dynamical horizon framework, which extends the earlier work on isolated horizons to time-dependent…
Some of the theoretical challenges posed by the general relativistic description of binary systems of compact objects (neutron stars or black holes) are reviewed. We recall the various ways one can use the theory of the motion, and of the…
Difference equations have many applications and play an important role in numerical analysis, probability, statistics, combinatorics, computer science, quantum consciousness, etc. We first prove that the partial differential equation is…
A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole…
Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDE models fail to…
Simulation of quasicircular compact binaries is a major goal in numerical relativity, as they are expected to constitute most gravitational wave observations. However, given that orbital eccentricity is not well-defined in general…
Randomness is ubiquitous in modern engineering. The uncertainty is often modeled as random coefficients in the differential equations that describe the underlying physics. In this work, we describe a two-step framework for numerically…
This work introduces the Elliptica pseudo-spectral code for generating initial data of binary neutron star systems. Building upon the recent Elliptica code update, we can now construct initial data using not only piecewise polytropic…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is…
Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and…
Models of gravitational waveforms from coalescing black-hole binaries play a crucial role in the efforts to detect and interpret the signatures of those binaries in the data of large-scale interferometers. Here we summarize recent models…
Solving dynamical problems in general relativity requires the full machinery of numerical relativity. Wilson has proposed a simpler but approximate scheme for systems near equilibrium, like binary neutron stars. We test the scheme on…
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…
In this exploratory study, we demonstrate the capability of the numerical-relativity code BAM to simulate fully relativistic black-hole binary-single and binary-binary encounters. While previous work has demonstrated the general capability…
We develop numerical algorithms to approximate positive solutions of elliptic boundary value problems with superlinear subcritical nonlinearity on the boundary of the form $-\Delta u + u = 0$ in $\Omega$ with $\frac{\partial u}{\partial…