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401-4503-68L  Reading Course: Reduced Basis Methods

SemesterHerbstsemester 2018
DozierendeR. Hiptmair
Periodizitäteinmalige Veranstaltung

KurzbeschreibungReduced Basis Methods (RBM) allow the efficient repeated numerical soluton of parameter depedent differential equations, which arise, e.g., in PDE-constrained optimization, optimal control, inverse problems, and uncertainty quantification. This course introduces the mathematical foundations of RBM and discusses algorithmic and implementation aspects.
Lernziel* Knowledge about the main principles underlying RBMs
* Familiarity with algorithms for the construction of reduced bases
* Knowledge about the role of and techniques for a posteriori error estimation.
* Familiarity with some applications of RBMs.
LiteraturMain reference:
Hesthaven, Jan S.; Rozza, Gianluigi; Stamm, Benjamin, Certified reduced basis methods for parametrized partial differential equations. SpringerBriefs in Mathematics, 2016

Supplementary reference:
Quarteroni, Alfio; Manzoni, Andrea; Negri, Federico, Reduced basis methods for partial differential equations. An introduction. Unitext 92, Springer, Cham, 2016.
Voraussetzungen / BesonderesThis is a reading course, which will closely follow the book by J. Hesthaven, G. Rozza and B. Stamm. Participants are expected to study particular sections of the book every week, which will then be discussed during the course sessions.