## MTHM607 - Computational Modelling and Simulation (2022)

MODULE TITLE CREDIT VALUE Computational Modelling and Simulation 30 MTHM607 Dr Markus Mueller (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11
 Number of Students Taking Module (anticipated) 20
DESCRIPTION - summary of the module content

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.

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) (see assessment section below for how ILOs will be assessed)
On successful completion of this module you should be able to:

Module Specific Skills and Knowledge:
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;

Discipline Specific Skills and Knowledge:
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;

Personal and Key Transferable/ Employment Skills and Knowledge:
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 - summary of the structure and academic content of the module
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 AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 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 260 Lecture and assessment preparation, computing, wider reading

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) 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 Assessment (e.g. duration/length) 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 Time Scale 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%.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener
Web-based and electronic resources:

Other resources:

N.A.

Type Author Title Edition Publisher Year ISBN Search
Set Curran, Mary Ann Life Cycle Assessment Handbook: A Guide for Environmentally Sustainable Products Wiley 2012 978-1-118-09972-8 [Library]
Set Forrester, J.W. Urban Dynamics Pegasus Communications 1969 978-1-883823-39-9 [Library]
Set Hairer, E., Lubich, C. & Wanner, G. Geometric Numerical Integration Springer 2002 978-3-540-30666-5 [Library]
Set Jones P.W. and Smith P. Stochastic Processes: methods and applications Arnold 2001 000-0-340-80654-0 [Library]
Set Leimkuhler, B. & Reich, S. Simulating Hamiltonian Dynamics Cambridge University Press 2004 978-0-511-61411-8 [Library]
Set Meadows, D.H. Limits to Growth University Books 1972 978-0-87663-165-2 [Library]
Set Meadows, D.H., Randers, J. & Meadows, D.L. The Limits to Growth: The 30-year Update Hill & Wang 2006 978-0809029570 [Library]
Set Morecroft, J. Strategic Modelling and Business Dynamics: A Feedback Systems Approach Wiley 2007 978-0-470-01286-4 [Library]
Set Norris, J. R. Markov Chains Cambridge University Press 1998 978-0521633963 [Library]
Set Pastor, J. Mathematical Ecology of Populations and Ecosystems Wiley 2008 9781405177955 [Library]
Set Sorensen, Bent Life-Cycle Analysis of Energy Systems: From Methodology to Applications Royal Society of Chemistry 2011 978-1-84973-145-4 [Library]
CREDIT VALUE ECTS VALUE 30 15
PRE-REQUISITE MODULES None None
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 7 No Wednesday 16 December 2020 Wednesday 25 May 2022
KEY WORDS SEARCH First principles; Mathematical modelling; Scientific programming; Simulation; Computation; Ecological dynamics; Environmental modelling