# ANNULÉ! CANCELLED! Computation of Gauss quadrature rules using a multi-level Parareal-like parallel approach applied to the Stieltjes procedure (Thibaut Lunet, University of Geneva)

17.03.2020 14:00 – 15:00

Gauss quadrature rules are nowadays a powerful tool to compute integrals with particular measures that arise in many scientific applications (e.g radiation transfer for the Earth’s atmosphere). To a given measure, one associates a sequence of orthogonal polynomials, uniquely determined by a set of three-term recurrence coefficients, from which one retrieves the quadrature nodes and weights using standard linear algebra methods. For some measures, the associated orthogonal polynomials are well known and studied (e.g Lagrange, Chebyshev, Laguerre, Hermite).

However, often non-classical measure arise in applications, for which the three-term recurrence coefficients need to be computed. To do so, W. Gautschi developed the "discretization method", that approximates the scalar product associated to the unknown measure, combined with the Stieltjes procedure to retrieve the three-term coefficients of the unknown measure.

In this talk, we present a new approach to perform the Stieltjes procedure based on Parareal, a well known algorithm allowing to compute the solution of time dependent problems while inducing parallelism in the time dimension. Thanks to that, one can compute in parallel the unknown three-term recursion coefficients, even if the Stieltjes procedure is originally a fully sequential algorithm. We illustrate this new approach using numerical experiments and some applications on measures appearing in physical

problems of interest for the scientific community.

### Lieu

ANNULÉ! CANCELLED!, Séminaire d'analyse numérique

### Organisé par

Section de mathématiques### Intervenant-e-s

Thibaut Lunet, University of Geneva, Switzerlandentrée libre