Related papers: Cauchy-perturbative matching and outer boundary co…
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D…
We consider the strategy of realizing the solution of a Cauchy problem with radial data as a limit of radial solutions to initial-boundary value problems posed on the exterior of vanishing balls centered at the origin. The goal is to gauge…
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…
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the…
We present a new approach for the Cauchy-characteristic extraction of gravitational radiation strain, news function, and the flux of the energy-momentum, supermomentum and angular momentum associated with the Bondi-Metzner-Sachs asymptotic…
We implement a code to find the gravitational news at future null infinity by using data from a Cauchy code as boundary data for a characteristic code. This technique of Cauchy-characteristic Extraction (CCE) allows for the unambiguous…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
A combination of some weighted energy estimates is applied for the Cauchy problem of quasilinear wave equations with the standard null conditions in three spatial dimensions. Alternative proofs for global solutions are shown including the…
We solve the problem of expressing the Weyl scalars $\psi $ that describe gravitational perturbations of a Kerr black hole in terms of Cauchy data. To do so we use geometrical identities (like the Gauss-Codazzi relations) as well as…
This paper studies the Cauchy problem for systems of semi-linear wave equations on $\mathbb{R}^{3+1}$ with nonlinear terms satisfying the null conditions. We construct future global-in-time classical solutions with arbitrarily large initial…
We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer…
A fully relativistic three-dimensional Cauchy-characteristic matching (CCM) algorithm is implemented for physical degrees of freedom in a numerical relativity code SpECTRE. The method is free of approximations and can be applied to any…
We review recent progress on the long-time regularity of solutions of the Cauchy problem for the water waves equations, in two and three dimensions. We begin by introducing the free boundary Euler equations and discussing the local…
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic…
A proper-time method for constructing models of dynamic gravitational-wave fields is presented. Using the proper-time method, analytical (not numerical) models of secondary gravitational waves are constructed as perturbative solutions of…
We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a…
We investigate the inverse Cauchy and data completion problems for elliptic partial differential equations in a bounded domain $D \subset \mathbb{R}^d$, $d \ge 2$, with a special emphasis on the steady-state heat conduction in anisotropic…
We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on…
We revisit the problem of gravitational-wave extraction in numerical relativity with gauge-invariant metric perturbation theory of spherical spacetimes. Our extraction algorithm allows the computation of even-parity (Zerilli-Moncrief) and…