401-0435-00L Computational Methods for Engineering Applications II
| Semester | Herbstsemester 2016 |
| Dozierende | S. Mishra |
| Periodizität | jährlich wiederkehrende Veranstaltung |
| Lehrsprache | Englisch |
Lehrveranstaltungen
| Nummer | Titel | Umfang | Dozierende | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 401-0435-00 V | Computational Methods for Engineering Applications II Lecture starts in the second week of the semester. | 2 Std. |
| S. Mishra | ||||||||||||
| 401-0435-00 U | Computational Methods for Engineering Applications II Exercises start in the second week of the semester. | 2 Std. |
| S. Mishra |
Katalogdaten
| Kurzbeschreibung | The course gives an introduction to the numerical methods for the solution of ordinary and partial differential equations that play a central role in engineering applications. Both basic theoretical concepts and implementation techniques necessary to understand and master the methods will be addressed. |
| Lernziel | At the end of the course the students should be able to: - implement numerical methods for the solution of ODEs (= ordinary differential equations); - identify features of a PDE (= partial differential equation) based model that are relevant for the selection and performance of a numerical algorithm; - implement the finite difference, finite element and finite volume method for the solution of simple PDEs using C++; - read engineering research papers on numerical methods for ODEs or PDEs. |
| Inhalt | Initial value problems for ODE: review of basic theory for ODEs, Forward and Backward Euler methods, Taylor series methods, Runge-Kutta methods, basic stability and consistency analysis, numerical solution of stiff ODEs. Two-point boundary value problems: Green's function representation of solutions, Maximum principle, finite difference schemes, stability analysis. Elliptic equations: Laplace's equation in one and two space dimensions, finite element methods, implementation of finite elements, error analysis. Parabolic equations: Heat equation, Fourier series representation, maximum principles, Finite difference schemes, Forward (backward) Euler, Crank-Nicolson method, stability analysis. Hyperbolic equations: Linear advection equation, method of characteristics, upwind schemes and their stability. Burgers equation, scalar conservation laws, shocks and rarefactions, Riemann problems, Godunov type schemes, TVD property. |
| Skript | Script will be provided. |
| Literatur | Chapters of the following book provide supplementary reading and are not meant as course material: - A. Tveito and R. Winther, Introduction to Partial Differential Equations. A Computational Approach, Springer, 2005. |
| Voraussetzungen / Besonderes | (Suggested) Prerequisites: Analysis I-III (for D-MAVT), Linear Algebra, CMEA I, basic familiarity with programming in C++. |
Leistungskontrolle
| Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird) | |
Leistungskontrolle als Semesterkurs | |
| ECTS Kreditpunkte | 4 KP |
| Prüfende | S. Mishra |
| Form | Sessionsprüfung |
| Prüfungssprache | Englisch |
| Repetition | Die Leistungskontrolle wird nur in der Session nach der Lerneinheit angeboten. Die Repetition ist nur nach erneuter Belegung möglich. |
| Prüfungsmodus | schriftlich 180 Minuten |
| Hilfsmittel schriftlich | Personal summary, 4 pages (2 sheets) A4 handwritten or machine-typed (single-spaced, font size at least 8 pt). |
| Diese Angaben können noch zu Semesterbeginn aktualisiert werden; verbindlich sind die Angaben auf dem Prüfungsplan. | |
Lernmaterialien
| Hauptlink | Lecture Homepage |
| Es werden nur die öffentlichen Lernmaterialien aufgeführt. | |
Gruppen
| Keine Informationen zu Gruppen vorhanden. |
Einschränkungen
| Keine zusätzlichen Belegungseinschränkungen vorhanden. |
Angeboten in
| Studiengang | Bereich | Typ | |
|---|---|---|---|
| Maschineningenieurwissenschaften Bachelor | Wahlfächer | W |  |