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Developments in numerical methods for problems governed by nonlinear partial differential equations underpin simulations with sound arguments in diverse areas of science and engineering. In this paper, we explore the regularization method…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
The cosmological stochastic gravitational-wave background produced by the mildly non-linear evolution of density fluctuations is analyzed, in the frame of an Einstein-de Sitter model, by means of a fully relativistic perturbation expansion…
A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary…
We have introduced a new method for computing gravitational-wave emission from nonspinning binaries which systematically unifies the various integrals arising in the Fourier expansions of post-Newtonian dynamics, providing a simple,…
The prospect of unprecedented high-quality data of gravitational waves in the upcoming decades demands a theoretical effort to optimally study and analyze the signals that next generation detectors will provide. Here we study the…
Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modelled using a variety of approximation schemes and numerical…
Modeling the stochastic gravitational wave background from various astrophysical sources is a key objective in view of upcoming observations with ground- and space-based gravitational wave observatories such as Advanced LIGO, VIRGO, eLISA…
The goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size $\epsilon$, is almost…
The main aim of this study is the comparison of gravitational waveforms obtained from numerical simulations which employ different numerical evolution approaches and different wave-extraction techniques. For this purpose, we evolve an…
We present a novel hybrid numerical-asymptotic boundary element method for high frequency acoustic and electromagnetic scattering by penetrable (dielectric) convex polygons. Our method is based on a standard reformulation of the associated…
Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in…
We consider the Cauchy problem for the wave equation in the whole space, R^n, with initial data which are distributions supported on finite sets. The main result is a precise description of the geometry of the sets of stationary points of…
This study investigates nonlinear gravity waves in the compressible atmosphere from the Earth's surface to the deep atmosphere. These waves are effectively described by Grimshaw's dissipative modulation equations which provide the basis for…
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…
A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained…
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…
We construct a class of linear partial differential equations describing general perturbations of non-rotating black holes in 3D Cartesian coordinates. In contrast to the usual approach, a single equation treats all radiative $\ell -m$…
The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasilinear elliptic--hyperbolic system of evolution…
We present new techniqes for evolving binary black hole systems which allow the accurate determination of gravitational waveforms directly from the wave zone region of the numerical simulations. Rather than excising the black hole…