Related papers: Binary black hole simulation with an adaptive fini…
The paper proposes and analyzes an efficient second-order in time numerical approximation for the Allen-Cahn equation, which is a second order nonlinear equation arising from the phase separation model. We firstly present a fully discrete…
A nonlinear Helmholtz (NLH) equation with high frequencies and corner singularities is discretized by the linear finite element method (FEM). After deriving some wave-number-explicit stability estimates and the singularity decomposition for…
We construct hairy rotating black hole solutions in three dimensional Einstein gravity coupled to a complex scalar field. When we turn on a real and uniform source on the dual CFT, the black hole is stationary with two Killing vectors and…
In this paper, we present three exact solutions to the Einstein field equations, each illustrating different black hole models. The first solution introduces a black hole with a variable equation of state, $P = k(r)\rho$, which can…
We present a new approach to studying the evolution of massive black hole binaries in a stellar environment. By imposing conservation of total energy and angular momentum in scattering experiments, we find the dissipation forces that are…
A new numerical method to construct binary black hole/neutron star initial data is presented. The method uses three spherical coordinate patches; Two of these are centered at the binary compact objects and cover a neighborhood of each…
We propose and analyze a hybridized discontinuous Galerkin (HDG) method for the spherically symmetric Einstein--scalar system in Bondi gauge. After rewriting the model as a local first-order PDE--ODE system by introducing suitable scaled…
In recent years, the immersed finite element methods (IFEM) introduced in \cite{Li2003}, \cite{Li2004} to solve elliptic problems having an interface in the domain due to the discontinuity of coefficients are getting more attentions of…
Extreme mass ratio binary systems, binaries involving stellar mass objects orbiting massive black holes, are considered to be a primary source of gravitational radiation to be detected by the space-based interferometer LISA. The numerical…
We consider a series of distorted black hole initial data sets, and develop techniques to evolve them using the linearized equations of motion for the gravitational wave perturbations on a Schwarzschild background. We apply this to 2D and…
An $hp$-adaptive continuous Galerkin finite element method is developed to analyze a static anti-plane shear crack embedded in a nonlinear, strain-limiting elastic body. The geometrically linear material is described by a constitutive law…
Solving Einstein's constraint equations for the construction of black hole initial data requires handling the black hole singularity. Typically, this is done either with the excision method, in which the black hole interior is excised from…
The close limit approximation of binary black hole is a powerful method to study gravitational-wave emission from highly non-linear geometries. In this work, we use it as a tool to model black hole spacetimes in theories of gravity with a…
We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data…
To fully unlock the scientific potential of upcoming gravitational wave (GW) interferometers, numerical relativity (NR) simulation accuracy will need to be greatly enhanced. We present three infrastructure-agnostic improvements to the…
We describe a numerical code that solves Einstein's equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used…
We derive the BPS type of first order differential equations for the rotating black hole solutions in the three-dimensional Einstein gravity coupled minimally with a self-interacting scalar field, using fake supersymmetry formalism. It…
We perform the first fully nonlinear numerical simulations of black-hole binaries with mass ratios 100:1. Our technique for evolving such extreme mass ratios is based on the moving puncture approach with a new gauge condition and an optimal…
Time evolution of a black hole lattice universe is simulated. The vacuum Einstein equations in a cubic box with a black hole at the origin are numerically solved with periodic boundary conditions on all pairs of opposite faces. Defining…
We consider unconstrained evolution schemes for the hyperboloidal initial value problem in numerical relativity as a promising candidate for the optimally efficient numerical treatment of radiating compact objects. Here, spherical symmetry…