MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Inspiral-merger-ringdown models for spinning black-hole binaries at the interface between analytical and numerical relativity

The long-sought direct detection of gravitational waves may only be a few years away, as a new generation of interferometric experiments of unprecedented sensitivity will start operating in 2015. These experiments will look for gravitational waves with frequencies from 10 to about 1000 Hz, thus targeting astrophysical sources such as coalescing binaries of compact objects, core collapse supernovae, and spinning neutron stars, among others. The search strategy for gravitational waves emitted by compact-object binaries consists in filtering the output of the detectors with template waveforms that describe plausible signals, as predicted by general relativity, in order to increase the signal-to-noise ratio. In this work, we modeled these systems through the effective-one-body approach to the general-relativistic 2-body problem. This formalism rests on the idea that binary coalescence is universal across different mass ratios, from the test-particle limit to the equal-mass regime. It bridges the gap between post-Newtonian theory (valid in the slow-motion, weak-field limit) and black-hole perturbation theory (valid in the small mass-ratio limit, but not limited to slow motion). The project unfolded along two main avenues of inquiry, with the goal of developing faithful inspiral-merger-ringdown waveforms for generic spinning, stellar-mass black-hole binaries. On the one hand, we studied the motion and gravitational radiation of test masses orbiting Kerr black holes in perturbation theory, with the goal of extracting strong-field information that can be incorporated into effective-one-body models. On the other hand, we worked at the interface between analytical and numerical relativity by calibrating effective-one-body models against numerical solutions of Einstein's equations, and testing their accuracy when extrapolated to different regions of the parameter space. In the course of this project, we also studied conservative effects of the 2-body dynamics, namely the periastron advance, and devised algorithms for generating realistic initial conditions for spinning, precessing black-hole binaries. The waveform models developed in this project will be employed in data-analysis pipelines and gravitational-wave searches of advanced LIGO and Virgo. In the near future, natural extensions of this work will be the inclusion of tidal effects in the comparable-mass regime (relevant for neutron-star/black-hole binaries), and spin precession in the test-particle limit