Fundamentals of certified reduced basis method for parametrized partial defferential equations and applications

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari

Ore 11:00–12:45
       14:15–16:00

Relatore:

• Gianluigi Rozza (SISSA Scuola Internazionale Superiore di Studi Avanzati -Trieste)

Abstract:
The course aims to provide the basic aspects of numerical approximation and efficient solution of parametrized PDEs for computational mechanics problem (heat and mass transfer, linear elasticity, viscous and potential flows).
We present reduced basis (RB) approximation and associated a posteriori error estimation for rapid and reliable solution of parametrized partial differential equations (PDEs). The focus is on rapidly convergent Galerkin approximations on a subspace spanned by ``snapshots''; rigorous and sharp a posteriori error estimators for the outputs/quantities of interest; efficient selection of quasi-optimal samples in general parameter domains; and Offline-Online computational procedures for rapid calculation in the many-query and real-time contexts.
We develop the RB methodology on affine elliptic coercive problems, suited to be extended for a wide range of (coercive and non-coercive, affine and non-affine) elliptic and parabolic PDEs with several applications from heat transfer, elasticity and fracture, acoustics, and fluid dynamics. We introduce the concept of affine and non-affine parametric dependence, some elements of approximation and algebraic stability.

Referente: Alberto Valli