Carlo Marcati: Catalogue data in Autumn Semester 2019

Name Dr. Carlo Marcati
URLhttps://people.math.ethz.ch/~cmarcati/
DepartmentMathematics
RelationshipLecturer

NumberTitleECTSHoursLecturers
401-3660-69LNumerical Analysis Seminar: Model Order Reduction and Reduced Bases for PDEs Information Restricted registration - show details
Number of participants limited to 5. Consent of Instructor needed.
4 credits2SC. Marcati
AbstractReduced Basis (RB) methods provide a technique to reduce the computational cost of problems described by partial differential equations which involve a wide range of parameters (parametric PDEs). Such problems are ubiquitous in science and engineering, both in the analysis of physical phenomena and in the design of new objects.
ObjectiveThe aim of this seminar is to review recent mathematical results on theoretical aspects of Reduced Basis
methods and to learn how model-order reduction techniques can be used to lower
computational cost in the solution of parametric PDEs.
ContentReduced Basis (RB) methods provide a technique to reduce the computational cost of
problems described by partial differential equations which involve a wide range
of parameters (parametric PDEs). Such problems are ubiquitous
in science and engineering, both in the analysis of physical phenomena and in
the design of new objects.

Building on top of classical
finite element approximations, RB methods split the work into a
computationally heavy offline phase and an online phase—where
only a reduced-order model needs to be solved—that can be executed almost in real-time.
The first phase involves computing the high-fidelity solutions to the PDE on a carefully
selected "training" set of parameters (so-called snapshots). The snapshots are then
used as a reduced basis (hence the name of the method) for the solution of problems on new parameters.
The methods used for the (quasi-)optimal selection of the basis are of independent interest
and shared with other model-order reduction techniques in statistics, approximation, and
data science.

The estimates on a priori RB errors are linked with the
approximability of the classes of solutions to the equations; furthermire, reduced approximations can be used as a theoretical tool
in the analysis of other reduction techniques.
LiteratureIntroductory textbooks.

[1] Jan S. Hesthaven, Gianluigi Rozza, and Benjamin Stamm, Certified reduced basis
methods for parametrized partial differential equations, SpringerBriefs in Mathemat-
ics, Springer, Cham; BCAM Basque Center for Applied Mathematics, Bilbao,
2016.

[2] Alfio Quarteroni, Andrea Manzoni, and Federico Negri, Reduced basis methods
for partial differential equations, Unitext, vol. 92, Springer, Cham, 2016.
Prerequisites / NoticeFormat of the seminar
The seminar format will be oral student presentations, combined with a written report.
Student presentations will be
based on a recent research paper selected in two meetings
at the start of the semester.