Computational Modelling
| Module title | Computational Modelling |
|---|---|
| Module code | EMGM007 |
| Academic year | 2025/6 |
| Credits | 30 |
| Module staff | Dr Markus Mueller (Lecturer) |
| Duration: Term | 1 | 2 | 3 |
|---|---|---|---|
| Duration: Weeks | 11 |
| Number students taking module (anticipated) | 20 |
|---|
Module description
The complexity of mathematical and computational models describing most natural and man-made systems necessitates modern numerical methods and analysis of computer simulations. In this module you will develop computational modelling and simulation skills within a context of essential, high-value applications, using state-of-the-art scientific computing software. The module will be problem focussed, taking real-world examples, and using these to inform your understanding and appreciation of the underlying modelling and simulation methods. The module will draw from a range of topics: large partial differential equation-based modelling of flows and fields; computer-aided systems analysis; stochastic systems; and approaches to modelling the environment and natural systems. You will communicate your models and findings to your peers and for assessment through reports, presentations and other digital media.
Module aims - intentions of the module
This module intends to introduce students to modern numerical algorithms design and computational techniques for mathematical modelling and simulation. You will explore modelling from first principles and the design and implementation of computational models using MATLAB or Python or similar high-level languages. The module follows a two-step learning process: (1) you are introduced to a modelling approach, and (2) you develop the approach within a substantive application.
Intended Learning Outcomes (ILOs)
ILO: Module-specific skills
On successfully completing the module you will be able to...
- 1. Formulate mathematical models from first principles;
- 2. Design modern numerical algorithms for mathematical modelling;
- 3. Use your programming skills in MATLAB or Python or similar high-level language to model challenging mathematical problems;
ILO: Discipline-specific skills
On successfully completing the module you will be able to...
- 4. Tackle a wide range of applied mathematical problems using modern numerical methods;
- 5. Model real-world problems and understand the principles underlying the techniques and when they are applicable;
ILO: Personal and key skills
On successfully completing the module you will be able to...
- 6. Show enhanced modelling, problem-solving and computing skills, and acquired tools that are widely used in mathematical modelling and simulation;
- 7. Communicate the value of modelling and simulation to a range of end users in life and environmental sciences, or energy engineering.
Syllabus plan
The aim of the module is to make sure the approaches are modern and current and so the specific modelling approaches may vary over time. Each modelling approach will be covered in blocks of intense learning and creating, in which an approach is introduced and then applied in mini-project based work. A selection of topics from the following list will be covered:
Fluids and flows
Part 1: Revision of numerical methods for Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs);
Part 2: Mathematical modelling and simulation of partial differential equations in fluid mechanics, fluid sloshing problem in Lagrangian particle-path and Eulerian coordinates;
Part 3: Introduction to Simulating Hamiltonian Systems: geometric and structure-preserving numerical methods; Stormer-Verlet and Shake-Rattle algorithms; Poisson-bracket discretisation;
Part 4: Symplectic integration and computational modelling of rigid-body dynamics, and mathematical fluid mechanics problems;
Computer-aided systems analysis
Part 1: Dynamical systems modelling and simulation: Modelling principles for natural and engineering systems; Equilibrium states analysis; Stability analysis; Applications from population ecology, resource analysis, engineering;
Part 2: Systems dynamics modelling and simulation: Levels and rates in systems dynamics; Causal and feedback loops; Diagrammatic process models; Applications from socio-economic systems, earth systems;
Part 3: Numerical methods: Finite element/finite difference/finite volume techniques;
Stochastic systems
Part 1: Markov processes and Markov chain modelling; Discrete-time Markov chains; Continuous-time Markov chains; Properties of Markov chains; Random walks;
Part 2: Time-series analysis and signal processing; Moving average models; Auto-regressive models; ARMA; ARIMA;
Part 3: Limit theorems; Central limit theorem; Law of large numbers; Ergodic theorems;
Populations and patterns
Part 1: Population modelling; Single species models; Interactive population models; Meta-population models; Spatio-temporal population models;
Part 2: Collective behaviour and movement dynamics; Agent-based modelling;
Part 3: Dynamics of Infectious Diseases; Compartmental models; Epidemiological networks and spatial epidemiology;
Part 4: Pattern formation; Reaction diffusion systems; Chemotaxis.
Learning activities and teaching methods (given in hours of study time)
| Scheduled Learning and Teaching Activities | Guided independent study | Placement / study abroad |
|---|---|---|
| 60 | 240 |
Details of learning activities and teaching methods
| Category | Hours of study time | Description |
|---|---|---|
| Scheduled Learning and Teaching Activities | 24 | Lectures and tutorials |
| Scheduled Learning and Teaching Activities | 6 | Student-led presentations |
| Scheduled Learning and Teaching Activities | 30 | Computer-based modelling workshops |
| Guided Independent Study | 240 | Lecture and assessment preparation, computing, wider reading |
Formative assessment
| Form of assessment | Size of the assessment (eg length / duration) | ILOs assessed | Feedback method |
|---|---|---|---|
| Exercises and/or mini-projects | 3 x 5 hours | 1-5, 7 | Oral |
Summative assessment (% of credit)
| Coursework | Written exams | Practical exams |
|---|---|---|
| 100 | 0 | 0 |
Details of summative assessment
| Form of assessment | % of credit | Size of the assessment (eg length / duration) | ILOs assessed | Feedback method |
|---|---|---|---|---|
| Coursework portfolio | 60 | Three project- or exercise-based reports (3 x 1,500 words or equivalent), each relating to a module topic | 1-7 | Written and verbal |
| Model design and demonstration | 40 | Design and implementation of a complex computational model (>500 lines of code and documentation) and its demonstration | 1-3, 5, 6 | Written and verbal |
Details of re-assessment (where required by referral or deferral)
| Original form of assessment | Form of re-assessment | ILOs re-assessed | Timescale for re-assessment |
|---|---|---|---|
| Coursework portfolio | Coursework (100%) | 1-7 | To be agreed by consequences of failure meeting |
| Model design and demonstration | Coursework (100%) | 1-3, 5, 6 | To be agreed by consequences of failure meeting |
Re-assessment notes
Deferral – if you miss an assessment for certificated reasons judged acceptable by the Mitigation Committee, you will normally be either deferred in the assessment or an extension may be granted. The mark given for a re-assessment taken as a result of deferral will not be capped and will be treated as it would be if it were your first attempt at the assessment.
Referral – if you have failed the module overall (i.e. a final overall module mark of less than 50%) you will be required to resubmit the original assessment as necessary. The mark given for a re-assessment taken as a result of referral will be capped at 50%.
Indicative learning resources - Basic reading
Basic reading:
- Hairer, E., Lubich, C. & Wanner, G., Geometric Numerical Integration, Springer, 2002. ISBN: 978-3-540-30666-5
- Leimkuhler, B. & Reich, S., Simulating Hamiltonian Dynamics, Cambridge University Press, 2004. ISBN: 978-0-511-61411-8
- Morecroft, J., Strategic Modelling and Business Dynamics: A Feedback Systems Approach, Wiley, 2007. ISBN: 978-0-470-01286-4
- Forrester, J.W., Urban Dynamics, Pegasus Communications, 1969. ISBN: 978-1-883823-39-9.
- Meadows, D.H., Limits to Growth, New York: University books, 1972. ISBN: 978-0-87663-165-2
- Meadows, D.H., Randers, J. & Meadows, D.L., The Limits to Growth: The 30-year Update, Hill & Wang, 2006. ISBN: 978-0809029570
- Sorensen, B., Life-Cycle Analysis of Energy Systems: From Methodology to Applications, Royal Society of Chemistry, 2011. ISBN: 978-1-84973-145-4
- Curran, M.A., Life Cycle Assessment Handbook: A Guide for Environmentally Sustainable Products, Wiley, 2012. ISBN: 978-1-118-09972-8
- Jones, P.W. & Smith, P., Stochastic Processes: methods and applications, Arnold, 2001. ISBN: 000-0-340-80654-0
- Norris, J.R., Markov Chains, Cambridge University Press, 1998. ISBN: 978-0521633963
- Pastor, J., Mathematical Ecology of Populations and Ecosystems, Wiley, 2008. ISBN: 978-1405177955
Web-based and electronic resources:
- ELE – College to provide hyperlink to appropriate pages
Other resources:
- N.A.
| Credit value | 30 |
|---|---|
| Module ECTS | 15 |
| Module pre-requisites | none |
| Module co-requisites | none |
| NQF level (module) | 7 |
| Available as distance learning? | No |
| Origin date | 01/05/2025 |
