401-0435-00L Computational Methods for Engineering Applications

Semester	Autumn Semester 2023
Lecturers	S. Mishra
Periodicity	yearly recurring course
Language of instruction	English

Courses

Number

Title

Hours

Lecturers

401-0435-00 V

Computational Methods for Engineering Applications

Offered for the last time in this form in the Autumn Semester 2023.

2 hrs

Fri

10:15-12:00

HG D 1.1 »

S. Mishra

401-0435-00 U

Computational Methods for Engineering Applications

Groups are selected in myStudies.
Offered for the last time in this form in the Autumn Semester 2023.

2 hrs

Mon	16:15-18:00	CLA E 4 »
	16:15-18:00	HG E 21 »
	16:15-18:00	ML F 34 »

S. Mishra

Catalogue data

Abstract	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.
Learning objective	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.
Content	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.
Lecture notes	Script will be provided.
Literature	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.
Prerequisites / Notice	(Suggested) Prerequisites: Analysis I-III (for D-MAVT), Linear Algebra, Models, Algorithms and Data: Introduction to Computing, 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 credits	4 credits
Examiners	S. Mishra
Type	session examination
Language of examination	English
Repetition	The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examination	written 180 minutes
Additional information on mode of examination	The exam for the course unit taught in the Autumn Semester 2023 is only offered in the Winter 2024 and Summer 2024 Examination Sessions.
Written aids	Personal 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.