Units

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Sample subject outline - Semester 2 2013

Note: Subject outlines often change before the semester begins. Below is a sample outline.

Rationale

An essential skill for practicing applied mathematicians and engineers is the derivation and implementation of computational models for solving the equations that govern many of the physical processes encountered in research and industry. Through the investigation of specific case studies developed in Matlab, the derivation of numerical techniques, the implementation of efficient algorithms and the visualisation of the simulation results, students undertaking this unit will develop an understanding of the value of computational mathematics.

Aims

The aim of this unit is to provide you with the opportunity to employ a number of the skills that you have developed in the discipline of computational mathematics, combining them in a coherent manner for solving topical and relevant real world problems.

Objectives

On successful completion of this unit you should be able to:

1. Formulate mathematical models and implement numerical algorithms for solving two-dimensional linear and nonlinear partial differential equations of the diffusion and advection-diffusion type.
2.Demonstrate a sound understanding of the basic concepts, knowledge and skills underlying numerical optimization and the implementation of numerical algorithms for solving specific problem types.
3. Apply programming skills to implement algorithms in MATLAB.
4. Engage critical and analytical thinking skills and communicate in writing appropriate to context.

Content

Content will be selected from the following topics:

1. Introduction to Krylov subspace methods for solving large, sparse, linear systems of equations. Preconditioning techniques. Restarting. Inexact Newton-Krylov methods for solving nonlinear systems.
2. Finite Volume Methods (FVM) for two-dimensional diffusion and advection-diffusion equations: Basic concepts of the FVM. Cell-centred and vertex-centred schemes. Treatment of source/sink terms and diffusion coefficients at control volume boundaries. Implementation of boundary and initial conditions. The treatment of advection/convection and the inclusion of these schemes within the framework of the FVM. Monotonicity arguments, stability, TVD schemes, upstream averaging, other averaging methods. A brief discussion of flux limiting.
3. Introduction to the unstructured mesh FVM and the control volume finite element (CVFE) method.
4. A broad survey of important topics in numerical optimisation with a concentrated focus on particular issues pertinent to the topic in question, including: Algorithmic and theoretical fundamentals. Line search and trust region methods. Classical unconstrained optimisation methods - Steepest descent, Newton, Quasi-Newton, Conjugate Gradients. Constrained optimisation. The KKT conditions. Active set methods, penalty functions. Specially structured problems. Nonlinear least squares. Quadratic Programmes. The Augmented Lagrangian. Sequential Quadratic Programming algorithms.

The above list of topics is not exclusive and will be supplemented by additional reading material as required and where possible to meet your needs and interests.

Approaches to Teaching and Learning

You are expected to attend lectures (3 hours per week) in which the course content will be presented and the computational techniques will be demonstrated.

Assessment

The assessment items in this unit are designed to determine your level of competency, measured against criteria, in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required.

Summative feedback will be provided throughout the semester with progressive posting of results either via Blackboard or email.

Assessment name: Project (applied)
Description: Individual Programming Assignments - There will be two individual Matlab programming projects, equally weighted, that cover the core material of the unit with a range of questions that are clearly defined and not open-ended. A detailed report summarising the overall study will also be submitted for assessment with each project. You will receive feedback on your performance in these projects to assist your learning. Note that the weighting listed below is a minimum - this item may count up to 80% (see unit coordinator for details).
Relates to objectives: 1, 2, 3 and 4.
Weight: 70%
Internal or external: Internal
Group or individual: Individual
Due date: Weeks 1 & 13

Assessment name: Examination (Theory)
Description: The final exam will assess you on your knowledge and ability in all sections of lecture content. Note that the weighting listed below is a maximum - this item may only count 20% (see unit coordinator for details).
Relates to objectives: 1, 2, 3 and 4.
Weight: 30%
Internal or external: Internal
Group or individual: Individual
Due date: Exam Period

Academic Honesty

QUT is committed to maintaining high academic standards to protect the value of its qualifications. To assist you in assuring the academic integrity of your assessment you are encouraged to make use of the support materials and services available to help you consider and check your assessment items. Important information about the university's approach to academic integrity of assessment is on your unit Blackboard site.

A breach of academic integrity is regarded as Student Misconduct and can lead to the imposition of penalties.

Resource materials

Texts:
There are no set texts for this unit. Some useful references are provided below.

References:
1. Bradie B (2006) A Friendly Introduction to Numerical Analysis, Prentice Hall
2. Saad Y (2003) Iterative Methods for Sparse Linear Systems, 2nd edition, SIAM, Philadelphia
3. Nocedal J & Wright SJ (2006) Numerical Optimization, 2nd edition, Springer
4. Morton KW & Mayers DF (1994) Numerical Solution of Partial Differential Equations, Cambridge University Press
5. Hoffman J (1993) Numerical Methods for Engineers and Scientists, McGraw-Hill Inc
6. Press WH, Teukolsky SA, Vetterling WT & Flannery BP, Numerical Recipes - The Art of Scientific Computing, 2nd edition, Cambridge University Press
7. Patankar SV (1980) Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing, McGraw Hill

There are many other good references available in the Library.

Risk assessment statement

There are no out of the ordinary risks associated with this unit since lectures and tutorials are held in ordinary lecture theatres or computer laboratories. Basic safety procedures in computer laboratories will be given to you when entering the computer laboratory for the first time. In addition, emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the university's health and safety web site http://www.hrd.qut.edu.au/healthsafety/healthsafe/index.jsp for further information.

Disclaimer - Offer of some units is subject to viability, and information in these Unit Outlines is subject to change prior to commencement of semester.

Last modified: 15-May-2012