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The parabolic-hyperbolic form of the constraints is integrated numerically. The applied numerical stencil is $4^{th}$ order accurate (in the spatial directions) while 'time'-integration is made by using the method of lines with a $4^{th}$…
There is a significant possibility that astrophysical black holes with nearly-extremal spins exist. Numerical simulations of such systems require suitable initial data. In this paper, we examine three methods of constructing…
The conformal method for constructing initial data for Einstein's equations is presented in both the Hamiltonian and Lagrangian picture (extrinsic curvature decomposition and conformal thin sandwich formalism, respectively), and advantages…
Initial data for evolving black-hole binaries can be constructed via many techniques, and can represent a wide range of physical scenarios. However, because of the way that different schemes parameterize the physical aspects of a…
We present an alternative approach to setting initial data in general relativity. We do not use a conformal decomposition, but instead express the 3-metric in terms of a given unit vector field and one unknown scalar field. In the case of…
We solve for single distorted black hole initial data using the puncture method, where the Hamiltonian constraint is written as an elliptic equation in R^3 for the nonsingular part of the metric conformal factor. With this approach we can…
We take further steps in the development of the characteristic approach to enable handling the physical problem of a compact self-gravitating object, such as a neutron star, in close orbit around a black hole. We examine different options…
With the goal of taking a step toward the construction of astrophysically realistic initial data for numerical simulations of black holes, we for the first time derive a family of fully general relativistic initial data based on…
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead…
Multi-dimensional distributions of discrete data that resemble ellipsoids arise in numerous areas of science, statistics, and computational geometry. We describe a complete algebraic algorithm to determine the quadratic form specifying the…
We present a set of boundary conditions for solving the elliptic equations in the Initial Data Problem for space-times containing a black hole, together with a number of constraints to be satisfied by the otherwise freely specifiable…
When using the black hole exclusion (horizon boundary condition) technique, $K$ is usually nonzero and spatially variable, so none of the special cases of York's conformal-decomposition algorithm apply, and the full 4-vector nonlinear York…
We show how the basic idea of parabolic Jacobi relaxation can be modified to obtain a new class of hyperbolic relaxation schemes that are suitable for the solution of elliptic equations. Some of the analytic and numerical properties of…
Numerical relativity, applied to collisions of black holes, starts with initial data for black holes already in each other's strong field. The initial hypersurface data typically used for computation is based on mathematical simplifying…
The purpose of this work is to construct asymptotically flat, time symmetric initial data with an apparent horizon of prescribed intrinsic and extrinsic geometry. To do this, we use the parabolic partial differential equation for…
We present a numerical scheme for determining hyperboloidal initial data sets for the conformal field equations by using pseudo-spectral methods. This problem is split into two parts. The first step is the determination of a suitable…
We present a new initial data formulation to solve the full set of Einstein equations for spacetimes that contain a black hole under general conditions. The method can be used to construct complete initial data for spacetimes (the full…
We construct approximate initial data for non-spinning black hole binary systems by asymptotically matching the 4-metrics of two tidally perturbed Schwarzschild solutions in isotropic coordinates to a resummed post-Newtonian 4-metric in…
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.…
Numerical simulations of binary black holes are accompanied by an initial spurious burst of gravitational radiation (called `junk radiation') caused by a failure of the initial data to describe a snapshot of an inspiral that started at an…