Scientific Computing I

Module IN2005

This Module is offered by TUM Department of Informatics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2011/2

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

available module versions
SS 2012WS 2011/2

Basic Information

IN2005 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Catalogue of non-physics elective courses
Total workloadContact hoursCredits (ECTS)
150 h 60 h 5 CP

Content, Learning Outcome and Preconditions

Content

The lecture includes the following scientific computing topics: - steps of the scientific computing simulation pipeline; - classification of mathematical models (discrete/continuous, deterministic/stochastic, etc.); - modeling with ordinary differential equations for the example of population growth; - numerical solution of systems of ordinary differential equations - modeling with partial differential equations for the example of fluid dynamics; - numerical discretization methods for partial differential equations (finite elements, time stepping, grid generation) - algorithms (grid traversal, data storage and access, matrix assembly) for the example of tree-structured grids - analysis of methods and results (adequacy and asymptotic behaviour of models; stability, consistency, accuracy, and convergence of numerical methods; sequential and parallel performance of simulation codes). An outlook will be given on the following topics: - implementation (architectures, parallel programming, load distribution, domain decomposition, parallel numerical methods) - visualization for the example of fluid dynamics - embedding in larger simulation environments (example fluidstructure interactions) - interactivity and computational steering

Learning Outcome

At the end of the module, participants know the steps of the scientific computing pipeline. They are able to classify and derive simple models, to analyse crticial points and asymptotic behaviour, and to apply common discretization methods as well as explicit and implicit time stepping schemes to a given PDE model. They know the basic approaches to analyse the adequacy and accuracy of numerical methods and underlying models. In addition, students are familiar with typical grid generation, grid traversal, data storage, matrix assembly, parallelization, and visualization issues and know examples for solution strategies and performance analysis measures.

Preconditions

Students should have basic knowledge in differential calculus and linear algebra.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

ArtSWSTitelDozent(en)Termine
VO 2 Scientific Computing 1 (IN2005) Mittwoch, 10:00–12:00

Learning and Teaching Methods

This module comprises lectures and accompanying tutorials. The contents of the lectures will be taught by talks and presentations. Students will be encouraged to study literature and to get involved with the topics in depth. In the tutorials, concrete problems will be solved - partially in teamwork - and selected examples will be discussed.

Media

Slides, whiteboard, exercise sheets

Literature

- A.B. Shiflet and G.W. Shiflet: Introduction to Computational Science, Princeton University Press - Golub, Ortega: Scientific Computing: An Introduction with Parallel Computing, Academic Press, 1993 - Strang: Computational Science and Engineering, Cambridge University Press, 2007 - Tveito, Winther: Introduction to Partial Differential Equations - A Computational Approach, Springer, 1998 - Boyce, DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 1992 (5th edition) - Stoer, Bulirsch: Introduction to Numerical Analysis, Springer, 1996

Module Exam

Description of exams and course work

Type of Assessment: exam In the exam students should prove to be able to identify a given problem and find solutions within limited time. The examination will completely cover the content of the lectures. The answers will require own formulations. In addition, questions requiring short calculations may be posed. Exam questions assess the participants' knowledge on the important steps of the scientific computing pipeline. They also test the capability to classify and derive simple models, to analyse critical points and asymptotic behaviour, and to apply common discretisation methods as well as explicit and implicit time stepping schemes to a given PDE model. The exam evaluates the students' ability to implement various ways of grid generation, grid traversal, data storage, matrix assembly, parallelisation, and visualization issues.

Exam Repetition

There is a possibility to take the exam at the end of the semester.

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