Advanced Solution Techniques (AdSolTech)5 ECTS
(englische Bezeichnung: Advanced Solution Techniques)
(Prüfungsordnungsmodul: Forschungsmodule Studienrichtung Modellierung, Simulation und Optimierung)

Lectures:

• • Advanced Solution Techniques
    (Vorlesung, 2 SWS, Peter Knabner, Wed, 8:00 - 10:00, Übung 5 / 01.254-128; Fri, 10:00 - 12:00, 04.363)
  • Exercises for Advanced Solution Techniques
    (Übung, 1 SWS, Peter Knabner, every 2. week Fri, 12:00 - 14:00, 04.363; single appointment on 29.5.2019, 10:00 - 12:00, 04.363; starting 17.5.2019)

Empfohlene Voraussetzungen:

Advanced Discretization Techniques

Inhalt:

• Krylov subspace methods for large non-symmetric systems of equations

• Multilevel methods, especially multigrid (MG) methods, nested and non-nested grid hierarchies

• Parallel numerics, especially domain decomposition methods

• Inexact Newton/Newton-Krylov methods for discretized nonlinear partial differential equations

• Preconditioning and operator-splitting methods

Lernziele und Kompetenzen:

Students

• are able to design application-specific own MG algorithms with the theory of multigrid methods and decide for which problems the MG algorithm is suitable to solve large linear systems of equations,

• are able to solve sparse nonlinear/non-symmetric systems of equations with modern methods (also with parallel computers),

• are able to develop under critical assessment complete and efficient methods for application-orientated problems.

Literatur:

• A. Quarteroni, A. Valli: Numerical Approximation of Partial Differential Equations

• P. Knabner, L. Angermann: Numerical Methods for Elliptic and Parabolic Differential Equations

• Further literature and scientific publications are announced during the lectures

Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:

1. Mathematik (Master of Science)
   (Po-Vers. 2015w | NatFak | Mathematik (Master of Science) | Gesamtkonto | Studienrichtung Modellierung, Simulation und Optimierung | Forschungsmodule Studienrichtung Modellierung, Simulation und Optimierung)

Studien-/Prüfungsleistungen:

Advanced solution techniques (Prüfungsnummer: 59011)

(englischer Titel: Advanced solution techniques)

Prüfungsleistung, mündliche Prüfung, Dauer (in Minuten): 15, benotet, 5.0 ECTS

Anteil an der Berechnung der Modulnote: 100.0 %

Prüfungssprache: Englisch

Erstablegung: SS 2019, 1. Wdh.: SS 2019

1. Prüfer:

Peter Knabner