Numerical Analysis 4 (Discretization Theory) - Interactive curriculae of TU Ilmenau
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| module properties module number 5792 - common information | |
|---|---|
| module number | 5792 |
| department | Department of Mathematics and Natural Sciences |
| ID of group | 2413 (Numerical Analysis and Information Processing) |
| module leader | Prof. Dr. Hans Babovsky |
| language | Deutsch |
| term | Wintersemester |
| previous knowledge and experience | Funktionalanalysis, Numerische Mathematik, Differentialgleichungen |
| learning outcome | Den Studierenden werden allgemeingültige Aussagen zur numerischen Lösung abstrakter Gleichungen in Banach- bzw. Hilbert-Räumen vermittelt. Sie werden damit befähigt, praxisrelevante Differenzial- und Integralgleichungen in endlichdimensionale Probleme zu transformieren und diese diskretisierten Gleichungen mit leistungsfähigen numerischen Verfahren zu lösen. |
| content | Diskretisierungsmethoden bei Operatorgleichungen (Konsistenz, Stabilität und Konvergenz, asymptotische Fehlerschätzung und Extrapolationsprinzip, iterative Defekt-Korrektur) Projektionsmethoden bei Operatorgleichungen (Galerkin- und Petrov-Galerkin-Methode, Spektral- und Pseudospektralmethoden, nichtlineare Probleme) Mehrgitter-Methoden für diskretisierte Gleichungen (Mehrgitter-Prinzip, V-Zyklus und W-Zyklus, Full Multigrid, Nichtlineare MGM, Full Approximation Scheme) Inexakte Newton-Methoden für diskretisierte Gleichungen ("Quasilinearisierung" contra Diskretisierung und Linearisierung, Jacobian-freie Methoden, forcing terms, Newton-Krylov-Löser). |
| media of instruction and technical requirements for education and examination in case of online participation | Folie, Tafel, Beamer, Computerunterstützung |
| literature / references | (1) Hoffmann, A.; Marx, B.; Vogt, W.: Mathematik für Ingenieure - Theorie und Numerik. Band 2, Pearson, Studium München 2006 (2) Trottenberg, U.; Oosterlee, C.W.; Schüller, A.: Multigrid. Academic Press, San Diego 2001 (3) Deuflhard, P.: Newton Methods for Nonlinear Problems. Springer, Berlin 2004 |
| evaluation of teaching | |
| Details reference subject | |
|---|---|
| module name | Numerical Analysis 4 (Discretization Theory) |
| examination number | 2400169 |
| credit points | |
| SWS | 3 |
| on-campus program (h) | |
| self-study (h) | |
| obligation | elective module |
| exam | none |
| details of the certificate | |
| link to Moodle course | |
| teacher | |
| signup details for alternative examinations | |
| maximum number of participants | |
| Details in degree program Master Mathematik und Wirtschaftsmathematik 2013 (WM), Master Mathematik und Wirtschaftsmathematik 2013 (AM) | |
|---|---|
| module name | Numerical Analysis 4 (Discretization Theory) |
| examination number | 2400169 |
| credit points | 4 |
| on-campus program (h) | 34 |
| self-study (h) | 86 |
| obligation | elective module |
| exam | none |
| details of the certificate | |
| link to Moodle course | |
| signup details for alternative examinations | |
| maximum number of participants | |