Postgraduate Course: Applied Numerical Algorithms (PGPH11037)
Course Outline
| School | School of Physics and Astronomy |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Not available to visiting students |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Credits | 10 |
| Home subject area | Postgraduate (School of Physics and Astronomy) |
Other subject area | None |
| Course website |
http://www.epcc.ed.ac.uk/msc/ |
Taught in Gaelic? | No |
| Course description | This course covers the fundamental issues surrounding the use of numerical methods to solve scientific and mathematical problems. It starts by describing the basics of the IEEE floating-point standard for real numbers, and associated issues of accuracy and exceptions. Basic techniques for representing mathematical equations in a numerical form are also described. A number of types of problem are then examined, along with the standard algorithms used to solve them. The most trusted libraries that implement these algorithms are introduced, and the motivation behind utilizing such standard algorithms and/or libraries is discussed. The course covers some of the most popular numerical libraries (eg. LAPACK and FFTW) and techniques (eg. direct and iterative linear equation solvers).
The most important example covered in the course is a convection-diffusion problem which is used to study the way that pollution released from a chimney disperses over land when there is a prevailing wind. The techniques used in deriving and solving the partial differential equations for this particular problem are applicable to a wide range of application areas in science and engineering. For example, similar techniques are commonly used in structural mechanics, fluid dynamics, astrophysics, weather modelling, and fundamental particle physics.
The course is taught using a variety of methods including formal lectures, practical exercises, programming examples and informal tutorial discussions. Lectures are supported by tutored practical sessions in order to reinforce the key concepts. |
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
| Additional Costs | None |
Course Delivery Information
| Not being delivered |
Summary of Intended Learning Outcomes
On completion of this course students should be able to:
On completion of this course students should be able to:
- Explain how real-valued quantities are represented on a computer as floating-point variables.
- Discuss the various sources of error relevant for computational simulation.
- Convert simple partial differential equations into numerical form.
- Select and implement the most appropriate method for solving a given system of linear equations.
- Use standard numerical libraries in their own codes.
- Diagnose when a numerical algorithm may be failing due to limited machine precision or floating-point exceptions. |
Assessment Information
| 100% examination consisting of a two hour exam |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Not entered |
| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | Not entered |
Contacts
| Course organiser | Dr Judy Hardy
Tel: (0131 6)50 6716
Email: |
Course secretary | Yuhua Lei
Tel: (0131 6) 517067
Email: |
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