Related papers: Cauchy-characteristic extraction in numerical rela…
Bondi-like (single-null) characteristic formulations of general relativity are used for numerical work in both asymptotically flat and anti-de Sitter spacetimes. Well-posedness of the resulting systems of partial differential equations,…
Adaptive techniques are crucial for successful numerical modeling of gravitational waves from astrophysical sources such as coalescing compact binaries, since the radiation typically has wavelengths much larger than the scale of the…
In this paper, we extend and simplify the methods in [13] to improve the results on uniqueness of the boundary determination for the Maxwell equation. In particular, we show that the electromagnetic parameters are uniquely determined to…
Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…
We discuss the issue of radiation extraction in asymptotically flat space-times within the framework of conformal methods for numerical relativity. Our aim is to show that there exists a well defined and accurate extraction procedure which…
We derive an analytical expression for extracting the gravitational waveforms at null infinity using the Weyl scalar $\psi_4$ measured at a finite radius. Our expression is based on a series solution in orders of 1/r to the equations for…
For 3-D quadratic quasilinear wave equations with or without null conditions in exterior domains, when the compatible initial data and Dirichlet boundary values are given, the global existence or the maximal existence time of small data…
Numerical simulation of evolution of a cluster of a finite number of gravitating bodies interacting only by their intrinsic gravity has been carried out. The goal of the study was to reveal the main characteristic phases of the spatial…
A method of solving the eikonal equation, in either flat or curved space-times, with arbitrary Cauchy data, is extended to the case of data given on a characteristic surface. We find a beautiful relationship between the Cauchy and…
This is the first paper in a series aimed to implement boundary conditions consistent with the constraints' propagation in 3D numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally…
We consider the Cauchy problem for an equation of Korteweg-de Vries-Kawahara type with initial data in the analytic Gevrey spaces. By using linear, bilinear and trilinear estimates in analytic Bourgain spaces, we establish the local…
Let $\Omega\subset \Bbb R^2$ be a bounded domain with $\partial\Omega\in C^\infty$ and $L$ be a positive number. For a three dimensional cylindrical domain $Q=\Omega\times (0,L)$, we obtain some uniqueness result of determining a…
Dynamical evolution of test fields in background geometry with a naked singularity is an important problem relevant to the Cauchy horizon instability and the observational signatures different from black hole formation. In this paper we…
In this thesis, I present the first numerical scheme able to perform Cauchy evolutions of asymptotically AdS spacetimes with reflective boundary conditions under no symmetry requirements on the solution. The scheme is based on the…
This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the…
We prove a long-term regularity result for three-dimensional gravity water waves with small initial data but nonzero initial vorticity. We consider solutions whose vorticity vanishes on the free boundary and use this to derive a system for…
The global characteristic initial value problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown…
Given a compact surface $\Gamma$ embedded in $\mathbb R^3$ with boundary $\partial \Gamma$, our goal is to construct a set of representatives for a basis of the relative cohomology group $H^1(\Gamma, \partial \Gamma^c)$, where $\Gamma^c$ is…
We introduce a new, open-source computational general relativity framework for the Wolfram Language called Gravitas, which boasts a number of novel and distinctive features as compared to the many pre-existing computational and numerical…
In this paper, we discuss the Cauchy Problem for the compressible isentropic Euler-Boltzmann equations with vacuum in radiation hydrodynamics. Firstly, we establish the local existence of regular solutions by the fundamental methods in the…