Course announcement: Reduced Basis Methods for Computational Mechanics, 28-30 April 2015,

[Emanuele Tuillier Illingworth]

Course: Advanced Topics in Numerical Solutions of PDEs (AMMA/MHPC)
*Topic: Reduced Basis Methods for Computational Mechanics, 28-30 April 2015*
web: 
https://www.math.sissa.it/course/phd-course/advanced-topics-numerical-solutions-pdes-0
Location: Room E, SISSA Miramare Campus,  April 28-30 April,  2015
Lecturer: Prof. Gianluigi Rozza, Exercises: Dr Francesco Ballarin, Dr 
Alberto Sartori

Timetable:

Lectures 9:30-11:00, 11:30-13:00, 14:30-16:00 Tuesday  28 April
Exercises 16:30-18:00 Tuesday 28 April
Lectures 9:30-11:00, 11:30-13:00 Wednesday 29 April
Exercises 14:30-16:00, 16:30-18:00 Wednesday 29 April
Lectures 9:30-11:00 Thursday 30 April
Seminar MHPC/mathLab 11:30-13:00 Thursday 30 April (Prof. Karsten Urban, 
University of  Ulm "Applications of Reduced Order Modelling")


*Learning outcomes/Objectives:*
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).

*Module Description:*
In this course 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 for a wide range of (coercive and 
non-coercive) elliptic and parabolic PDEs with
several examples drawn 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. Finally, we consider application of RB techniques to 
parameter estimation, optimization, optimal control,
and a comparison with other reduced order techniques, like Proper 
Orthogonal Decomposition.
Some tutorials are prepared for the course based on FEniCS and Python. 
Lecture notes, slides and reading material will be provided during the 
classes.

/A seminar by Prof. Karsten Urban (Ulm University, Germany) will be 
given on taught topics on April 30, 2015 (morning, 11:30 am)./

*Topics/Syllabus*

-Introduction to RB methods, offline-online computing, elliptic coercive 
affine problems
-Sampling, greedy algorithm, POD
-A posteriori error bounds
-Primal-Dual Approximation
-Time dependent problems: POD-greedy sampling
-Non-coercive problems
-Approximation of coercivity and inf-sup parametrized constants
-Geometrical parametrization
-Reference worked problems
-Examples of Applications in CFD