Applied Numerical Algorithms (P01657)

? Credit Points : 10 ? SCQF Level : 11 ? Acronym : PHY-P-HPCNumAlg

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

? Pre-requisites : Only postgraduates or final year MPhys students with suitable computational background, subject to space restrictions and agreement with relevant Programme Coordinator.

Subject Areas

Home subject area

Postgraduate (School of Physics), (School of Physics, Schedule Q)

Delivery Information

? Normal year taken : Postgraduate

? Delivery Period : Block 5 and beyond

? Contact Teaching Time : 20 hour(s) per week for 1 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	09:00	17:00	KB

Summary of Intended Learning Outcomes

On completion of this course students should be able to:

- Discuss the relative advantages and disadvantages of using fixed-point, floating-point and interval arithmetic.
- Diagnose when a numerical algorithm may be failing due to limited machine precision.
- Select the most appropriate method for solving a given system of linear equations.
- Use standard numerical libraries in their own codes.