Related papers: Construction of high precision numerical single an…
We introduce a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a…
This paper addresses several geometric inverse problems for some linear parabolic systems where the initial data (and sometimes also the coefficients of the equations) are unknown. The goal is to identify a subdomain within a…
In this paper we analyze a homogeneous parabolic problem with initial data in the space of regular Borel measures. The problem is discretized in time with a discontinuous Galerkin scheme of arbitrary degree and in space with continuous…
Numerical simulations of binary black holes---an important predictive tool for the detection of gravitational waves---are computationally expensive, especially for binaries with high mass ratios or with rapidly spinning constituent holes.…
(Abridged) By asymptotically matching a post-Newtonian (PN) metric to two tidally perturbed Schwarzschild metrics, we generate approximate initial data (in the form of a 4-metric) for a nonspinning black hole binary in a circular orbit. We…
The notion of the characteristic Lie algebra of the discrete hyperbolic type equation is introduced. An effective algorithm to compute the algebra for the equation given is suggested. Examples and further applications are discussed.
This paper is devoted to the computation of compact binaries composed of one black hole and one neutron star. The objects are assumed to be on exact circular orbits. Standard 3+1 decomposition of Einstein equations is performed and the…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are weaker regularity assumptions for the boundary data and…
We argue that a primordial black hole is a natural and unique candidate for all dark matter. We show that, in a smooth-hybrid new double inflation model, a right amount of the primordial black holes, with a sharply-defined mass, can be…
We look for physically realistic initial data in numerical relativity which are in agreement with post-Newtonian approximations. We propose a particular solution of the time-symmetric constraint equation, appropriate to two momentarily…
We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for…
We describe a procedure for constructing initial data for boosted black holes in the moving-punctures approach to numerical relativity that endows the initial time slice from the outset with trumpet geometry within the black hole interiors.…
We investigate the well-posedness of the characteristic initial-boundary value problem for the Einstein equations in Bondi-like coordinates (including Bondi, double-null and affine). We propose a definition of strong hyperbolicity of a…
In this note, we construct an algorithm that, on input of a description of a structurally stable planar dynamical flow $f$ defined on the closed unit disk, outputs the exact number of the (hyperbolic) equilibrium points and their locations…
The orbital motion of inspiralling and coalescing black hole binaries can be investigated using a variety of approximation schemes and numerical methods within general relativity: post-Newtonian expansions, black hole perturbation theory,…
We present a new numerical method for the construction of quasiequilibrium models of black hole-neutron star binaries. We solve the constraint equations of general relativity, decomposed in the conformal thin-sandwich formalism, together…
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…
Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper, we provide…
We introduce a new framework for constructing black hole solutions that are holographically dual to strongly coupled field theories with explicitly broken translation invariance. Using a classical gravitational theory with a continuous…