401-0435-00L  Computational Methods for Engineering Applications II

SemesterHerbstsemester 2016
DozierendeS. Mishra
Periodizitätjährlich wiederkehrende Veranstaltung


401-0435-00 VComputational Methods for Engineering Applications II
Lecture starts in the second week of the semester.
2 Std.
Di15:15-17:00HG F 7 »
S. Mishra
401-0435-00 UComputational Methods for Engineering Applications II
Exercises start in the second week of the semester.
2 Std.
Di17:15-19:00HG G 26.1 »
Do10:15-12:00HG E 33.1 »
10:15-12:00HG F 26.5 »
10:15-12:00HG G 26.5 »
S. Mishra


KurzbeschreibungThe 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.
LernzielAt 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.
InhaltInitial 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.
SkriptScript will be provided.
LiteraturChapters 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++.


Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs
ECTS Kreditpunkte4 KP
PrüfendeS. Mishra
RepetitionDie Leistungskontrolle wird nur in der Session nach der Lerneinheit angeboten. Die Repetition ist nur nach erneuter Belegung möglich.
Prüfungsmodusschriftlich 180 Minuten
Hilfsmittel schriftlichPersonal 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.


HauptlinkLecture Homepage
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