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

 Semester Autumn Semester 2022 Lecturers S. Mishra Periodicity yearly recurring course Language of instruction English

### Courses

NumberTitleHoursLecturers
401-0435-00 VComputational Methods for Engineering Applications
Lecture starts in the second week of the semester.
2 hrs
 Mon 10:15-12:00 CAB G 51 »
S. Mishra
401-0435-00 UComputational Methods for Engineering Applications
Groups are selected in myStudies.
Exercises start in the second week of the semester.
2 hrs
 Mon 17:15-19:00 CHN G 46 » Thu 10:15-12:00 CLA E 4 » 10:15-12:00 HG E 33.1 » 10:15-12:00 LFW C 11 »
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. 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 only offered in the session after the course unit. Repetition only possible after re-enrolling. Mode of examination written 180 minutes 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.

### Learning materials

 Main link Lecture Homepage Only public learning materials are listed.

### Groups

401-0435-00 UComputational Methods for Engineering Applications
 Mon 17:15-19:00 CHN G 46 »
GroupsG-01
 Thu 10:15-12:00 HG E 33.1 »
G-02
 Thu 10:15-12:00 CLA E 4 »
G-03
 Thu 10:15-12:00 LFW C 11 »

### Restrictions

 There are no additional restrictions for the registration.

### Offered in

ProgrammeSectionType
Mechanical Engineering BachelorElectivesW