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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…
As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised…
Using the Reduced Basis approach, we efficiently compress and accurately represent the space of waveforms for non-precessing binary black hole inspirals, which constitutes a four dimensional parameter space (two masses, two spin…
We develop a unified framework for the design and analysis of high-order nonconforming virtual element methods for nonlinear fourth-order reaction--diffusion problems in two dimensions, with emphasis on clamped, Navier, and…
Apparent horizon plays an important role in numerical relativity as it provides a tool to characterize the existence and properties of black holes on three-dimensional spatial slices in 3+1 numerical spacetimes. Apparent horizon finders…
Odometry in adverse weather conditions, such as fog, rain, and snow, presents significant challenges, as traditional vision and LiDAR-based methods often suffer from degraded performance. Radar-Inertial Odometry (RIO) has emerged as a…
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…
We describe in detail full numerical and perturbative techniques to compute the gravitational radiation from intermediate-mass-ratio black-hole-binary inspirals and mergers. We perform a series of full numerical simulations of nonspinning…
We present a numerical study of type IIB supergravity solutions with varying Ramond-Ramond flux. We construct solutions that have a regular horizon and contain nontrivial five- and three-form fluxes. These solutions are holographically dual…
The computations of numerical relativity make use of (3+1)- decompositions of Einstein field equations. We examine the conceptual characteristics of this method; instances of compact-star binaries are considered. The preeminent role of the…
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 propose a novel numerical method for solving multi-dimensional, special relativistic Boltzmann equations for neutrinos coupled to hydrodynamics equations. It is meant to be applied to simulations of core-collapse supernovae. We handle…
We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the…
We develop a numerical scheme for solving a fully special relativistic resistive radiation magnetohydrodynamics. Our code guarantees conservations of total mass, momentum and energy. Radiation energy density and radiation flux are…
We present a novel implicit numerical implementation of the parabolic-hyperbolic formulation of the constraints of general relativity. The proposed method is unconditionally stable, has the advantage of not requiring the imposition of any…
We review in a pedagogical fashion the 3+1-split which serves to put Einstein's equations into the form of a dynamical system with constraints. We then discuss the constraint equations under the simplifying assumption of time-symmetry.…
We produce the first astrophysically-relevant numerical binary black hole gravitational waveform in a higher-curvature theory of gravity beyond general relativity. We simulate a system with parameters consistent with GW150914, the first…
The deviations of non-linear perturbations of black holes from the linear case are important in the context of ringdown signals with large signal-to-noise ratio. To facilitate a comparison between the two we derive several results of linear…
We present and assess a Bayesian method to interpret gravitational wave signals from binary black holes. Our method directly compares gravitational wave data to numerical relativity simulations. This procedure bypasses approximations used…
We introduce Residue Hyperdimensional Computing, a computing framework that unifies residue number systems with an algebra defined over random, high-dimensional vectors. We show how residue numbers can be represented as high-dimensional…