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

SemesterAutumn Semester 2015
LecturersS. Mishra
Periodicityyearly recurring course
Language of instructionEnglish


401-0435-00 VComputational Methods for Engineering Applications II2 hrs
Tue15:15-17:00HG F 7 »
S. Mishra
401-0435-00 UComputational Methods for Engineering Applications II2 hrs
Tue17:15-19:00HG D 5.3 »
Thu10:15-12:00CLA E 4 »
10:15-12:00HG D 1.1 »
10:15-12:00HG D 7.2 »
10:15-12:00HG E 22 »
10:15-12:00HG E 33.1 »
10:15-12:00HG F 26.5 »
10:15-12:00HG G 26.5 »
10:15-12:00LFW E 11 »
10:15-12:00LFW E 13 »
10:15-12:00ML J 34.1 »
24.09.10:15-12:00HG E 5 »
S. Mishra

Catalogue data

AbstractThe 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.
ObjectiveAt 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.
ContentInitial value problems for ODE: review of basic theory for ODEs, Forward and Backward Euler methods, Taylor series methods, Runge-Kutta methods, multi-step methods, predictor-corrector 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.
Lecture notesScript will be provided.
LiteratureChapters 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.
Prerequisites / Notice(Suggested) Prerequisites:
Analysis I-III (for D-MAVT), Linear Algebra, CMEA I, basic familiarity with programming in C++.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits4 credits
ExaminersS. Mishra
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is only offered in the session after the course unit. Repetition only possible after re-enrolling.
Mode of examinationwritten 180 minutes
Written aidsPersonal summary, 4 pages (2 sheets) A4 handwritten or machine-typed (single-spaced, font size at least 8 pt).
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

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Offered in

Mechanical Engineering BachelorElectivesWInformation