2019/20 Taught Postgraduate Module Catalogue

MECH5315M Engineering Computational Methods

15 creditsClass Size: 200

Module manager: Prof Harvey M Thompson
Email: H.M.Thompson@leeds.ac.uk

Taught: Semester 1 View Timetable

Year running 2019/20

Pre-requisite qualifications

Students should have a good understanding of calculus as taught e.g. in MECH1520 Engineering Mathematics. This includes knowledge of differentiation, integration, matrices and vectors, basic Fourier analysis, eigenvalues, Taylor series and differential equations. Basic programming experience in MATLAB or another language like Python, C++ or FORTRAN is not mandatory but highly desirable.

Pre-requisites

 MECH1520 Engineering Mathematics

Module replaces

MECH 5510M Computational & Experimental Methods

This module is not approved as an Elective

Module summary

The module introduces students to the basic computational methods used to solve engineering problems modelled by ordinary differential equations and parabolic or hyperbolic partial differential equations. They will also learn how to implement the learned methods in practice. Engineering simulation software packages rely on computational methods and a good understanding is crucial to knowledgeably use them.

Objectives

On successful completion of this module, students should understand the basic concepts of computational methods used in engineering. In order to fulfil this goal, the module will be divided into three sections.
The first section discusses numerical methods for ordinary differential equations, extending knowledge from undergraduate engineering mathematics.
The second section will acquaint the students with examples of dissipative partial differential equations, e.g. for modelling heat diffusion, and how to solve them numerical.
The third section is concerned with hyperbolic partial differential equations used to model e.g. waves.
In addition to mathematical skills, the students will also learn how to implement the learned methods in practice via computer laboratory work.

Learning outcomes
After successful completion of the module, students will:
1. Have a good overview of different numerical techniques used to solve differential equations;
2. Know the most important characteristics of each technique and in particular its limitations;
3. Be able to translate simple numerical algorithms into MATLAB code;
4. Have learned how to investigate performance of a numerical algorithm by running numerical examples.
Upon successful completion of this module the following UK-SPEC learning outcome descriptors are satisfied:

A comprehensive understanding of the relevant scientific principles of the specialisation (SM1m, SM7M)
Knowledge and understanding of mathematical and statistical methods necessary to underpin education in medical engineering and to enable them to apply a range of mathematical and statistical methods, tools and notations proficiently and critically in the analysis and solution of engineering problems (SM2m)
A comprehensive knowledge and understanding of mathematical and computational models relevant to the engineering discipline, and an appreciation of their limitations (SM5m)
Understanding of concepts relevant to the discipline, some from outside engineering, and the ability to evaluate them critically and to apply them effectively, including in engineering projects (SM6m, SM9M)
A critical awareness of current problems and/or new insights most of which is at, or informed by, the forefront of the specialisation (SM8M)
Understanding of engineering principles and the ability to apply them to undertake critical analysis of key engineering processes (EA1m)
Ability to identify, classify and describe the performance of systems and components through the use of analytical methods and modelling techniques (EA2)
Ability both to apply appropriate engineering analysis methods for solving complex problems in engineering and to assess their limitations (EA3m, EA6M)
Ability to use fundamental knowledge to investigate new and emerging technologies (EA5m)
Ability to collect and analyse research data and to use appropriate engineering analysis tools in tackling unfamiliar problems, such as those with uncertain or incomplete data or specifications, by the appropriate innovation, use or adaptation of engineering analytical methods (EA7M)
Understanding of the use of technical literature and other information sources (P4)
Ability to work with technical uncertainty (P8)
A thorough understanding of current practice and its limitations, and some appreciation of likely new developments (P9m)
Apply their skills in problem solving, communication, information retrieval, working with others, and the effective use of general IT facilities (G1)

Syllabus

1. Basic programming methodology for computational methods.
2. Initial value problems and ordinary differential equations: Euler method, Runge-Kutta methods and multi-step methods.
3. Parabolic partial differential equations: finite difference methods, spectral methods.
4. Hyperbolic partial differential equations: finite difference methods, finite volumes.

Teaching methods

 Delivery type Number Length hours Student hours Lecture 32 1.00 32.00 Practical 6 2.00 12.00 Private study hours 106.00 Total Contact hours 44.00 Total hours (100hr per 10 credits) 150.00

Private study

2 hours of preparation for and study after each lecture for a total of 64 hours.
2 hours of preparation for and study after each practical for a total of 12 hours.
Two 4 page long exercises plus programming requiring 15 hours each for a total of 30 hours.

Opportunities for Formative Feedback

Students have to complete two computer exercises. These will demonstrate understanding of both the methods as well as programming skills and allow to monitor progress throughout the course. In addition, ungraded multiple choice tests will be provided through VLE to also monitor progress.

Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Report Programs plus 4 pages report 50.00 Report Programs plus 4 pages report 50.00 Total percentage (Assessment Coursework) 100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated