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This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…
Building initial conditions for generic binary black-hole evolutions without initial spurious eccentricity remains a challenge for numerical-relativity simulations. This problem can be overcome by applying an eccentricity-removal procedure…
Hyperspectral unmixing, the process of estimating a common set of spectral bases and their corresponding composite percentages at each pixel, is an important task for hyperspectral analysis, visualization and understanding. From an…
COCAL is a code for computing equilibriums or quasiequilibrium initial data of single or binary compact objects based on finite difference methods. We present the results of supplementary convergence tests of COCAL code using time symmetric…
We initiate a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory. We focus primarily on asymptotically flat stationary vacuum solutions, where we…
We present new sequences of general relativistic, quasiequilibrium black hole-neutron star binaries. We solve for the gravitational field in the conformal thin-sandwich decomposition of Einstein's field equations, coupled to the equations…
At the beginning of binary black hole simulations, there is a pulse of spurious radiation (or junk radiation) resulting from the initial data not matching astrophysical quasi-equilibrium inspiral exactly. One traditionally waits for the…
We study the spherically symmetric collapse of a real, minimally coupled, massive scalar field in an asymptotically Einstein-de Sitter spacetime background. By means of an eikonal approximation for the field and metric functions, we obtain…
The construction of high-resolution shock-capturing schemes is vital in producing highly accurate gravitational waveforms from neutron star binaries. The entropy based flux limiting (EFL) scheme is able to perform fast converging binary…
Several applications of spectral methods to problems related to the relativistic astrophysics of compact objects are presented. Based on a proper definition of the analytical properties of regular tensorial functions we have developed a…
Adaptive multilevel finite element methods are developed and analyzed for certain elliptic systems arising in geometric analysis and general relativity. This class of nonlinear elliptic systems of tensor equations on manifolds is first…
The aim of this article is to construct initial data for the Einstein equations on manifolds of the form R n+1 x T m , which are asymptotically flat at infinity, without assuming any symmetry condition in the compact direction. We use the…
Sequences of initial-data sets representing binary black holes in quasi-circular orbits have been used to calculate what may be interpreted as the innermost stable circular orbit. These sequences have been computed with two approaches. One…
This thesis describes a numerical study of binary boson stars within the context of an approximation to general relativity. The approximation we adopt places certain restrictions on the dynamical variables of general relativity (conformal…
The hyperboloidal initial value problem is addressed in the context of Numerical Relativity, motivated by its use of hyperboloidal slices - smooth spacelike slices that reach future null infinity, the "place" in spacetime where radiation is…
In this paper, a shallow Ritz-type neural network for solving elliptic equations with delta function singular sources on an interface is developed. There are three novel features in the present work; namely, (i) the delta function…
Reducing orbital eccentricity in numerical relativity simulations of binary black holes is essential for producing astrophysically relevant gravitational wave models, as many of these systems are expected to be near-circular in nature.…
Mounting evidence indicates that some of the gravitational wave signals observed by the LIGO/Virgo/KAGRA observatories might arise from eccentric compact object binaries, increasing the urgency for accurate waveform models for such systems.…
With the example of the spherically symmetric scalar wave equation on Minkowski space-time we demonstrate that a fully pseudospectral scheme (i.e. spectral with respect to both spatial and time directions) can be applied for solving…
Newtonian and post-Newtonian (PN) calculations suggest that each spherical harmonic mode of the gravitational waveforms (radiation) emitted by eccentric binaries can be further decomposed into several eccentricity-induced modes (indexed by…