Advanced Numerics of Partial Differential Equations

Lecture "Reduced Basis Methods"

Information

Lecture: Wed. 9:45-11:15, Fr. 8:00-9:30, PWR 57, SR 7.122

Exercises: Wed. 11:30-13:00, PWR 57, SR 7.122

Time Period: Wed. 10.4.2019 - Fr. 19.7.2019

see ILIAS-page

Content:

Various methods exist for the numerical solution of partial differential equations, which mostly lead to high dimensional and computationally demanding problems. These computational requirements are even higher, if the discretized problems need to be solved repeatedly, e.g. under parameter variation in the differential equations. This is relevant in cases of parameter studies, parameter identification, design or optimization. Reduced basis methods allow the efficient treatment of such parametric problems. Based on special solutions for selected parameters, the so called snapshots, low dimensional approximation spaces are constructed, which are denoted reduced basis spaces. Galerkin projection leads to a reduced computational model, which allows parameter variation and can be rapidly solved. The model error can be quantified by corresponding a-posteriori error analysis. This lecture gives an introduction in this class of model reduction techniques. 

Literature:

see ILIAS-page

Curricula:

M.Sc. Mathematics, M.Sc. SimTech but as well as "vorgezogeses Mastermodul" for    B.Sc. Mathematics. Also suitable for other study programmes.

Prerequisites:

Programming knowledge, basic knowledge of numerics of PDEs. The lecture NUMPDE is NOT required.

Credits and Exam:

see ILIAS-page

Kontakt

Dieses Bild zeigt  Bernard Haasdonk
Prof. Dr.

Bernard Haasdonk

Leiter der Abteilung Numerische Mathematik
Studiendekan B.Sc./M.Sc. Mathematik

Zum Seitenanfang