MECH5315M Engineering Computational Methods

15 creditsClass Size: 200

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

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2024/25

Pre-requisite qualifications

Students should have a good understanding of calculus as taught in UG Engineering Mathematics and Mechanics. This includes knowledge of differentiation, integration, matrices and vectors, basic Fourier analysis, eigenvalues, Taylor series and differential equations

Module replaces

MECH5510M 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 methods through practical programming experience.

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 numerically.
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
On successful completion of the module students will have demonstrated the following learning outcomes relevant to the subject:

On completion of this module, students should be able to:
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 Engineering Council Accreditation of Higher Education Programmes (AHEP) learning outcome descriptors (fourth edition) are satisfied:
5. Apply a comprehensive knowledge of mathematics, statistics, natural science and engineering principles to the solution of complex problems. Much of the knowledge will be at the forefront of the particular subject of study and informed by a critical awareness of new developments and the wider context of engineering. (M1)
6. Formulate and analyse complex problems to reach substantiated conclusions. This will involve evaluating available data using first principles of mathematics, statistics, natural science and engineering principles, and using engineering judgment to work with information that may be uncertain or incomplete, discussing the limitations of the techniques employed. (M2)
7. Select and apply appropriate computational and analytical techniques to model complex problems, discussing the limitations of the techniques employed. (M3)

Skills Learning Outcomes
On successful completion of the module students will have demonstrated the following skills:

a. Communication,
b. technical/IT skills,
c. problem solving and analytical skills,
d. Programming,
e. computational mechanics

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, spectral methods, method of characteristics.

Methods of Assessment

We are currently refreshing our modules to make sure students have the best possible experience. Full assessment details for this module are not available before the start of the academic year, at which time details of the assessment(s) will be provided.

Assessment for this module will consist of;

2 x Report

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

Opportunities for Formative Feedback

Students will attend 6 2-hour computer practical sessions where formative feedback on progress and problems in understanding can be provided too.