# 2022/23 Taught Postgraduate Module Catalogue

## COMP5930M Scientific Computation

### 15 creditsClass Size: 150

Module manager: Dr Toni Lassila
Email: T.Lassila@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2022/23

This module is not approved as an Elective

### Module summary

Understand the range of problems that can be formulated as nonlinear equation systems.Consider standard algorithms for these problems and the efficiency of their implementation.Demonstrate how state-of-the-art algorithms deliver gains in efficiency and allow the solution of large, sparse systems of nonlinear equations.

### Objectives

On completion of this module, students should be able to:
- understand the role of computational methods in Scientific Computing and the importance of reliability, efficiency and accuracy;
- demonstrate awareness of the state-of-the-art in Scientific Computing algorithms for the solution of nonlinear problems;
- understand the practical issues associated with implementation in code;
- demonstrate awareness of typical applications for such software.

Learning outcomes
1. Formulate systems of nonlinear equations to solve challenging real-world problems arising from engineering and science
2. Analyse a given nonlinear equation and choose and implement the best numerical method for the problem
3. Implement algorithmic solutions to solve computational differential equation problems based on mathematical theory
4. Analyse computational linear algebra problems and identify the most efficient solution algorithm for large problems
5. Develop a broad understanding of the theory of numerical analysis and its applications to the solution of nonlinear and differential equations

### Syllabus

- Numerical solution of a single nonlinear equation.
- Extension of the algorithms to systems of nonlinear equations and reduction to a series of linear equation systems.
- The concept of nonlinear partial differential equations and example applications.
- The need for reliable, efficient and accurate numerical approximation and how this results in discrete systems of nonlinear equations.
- Efficient direct and iterative solution algorithms for large, sparse, linear equation systems.
- Application to problems from classical fluid mechanics and other nonlinear partial differential equations.

### Teaching methods

 Delivery type Number Length hours Student hours Lectures 20 1.00 20.00 Tutorial 10 1.00 10.00 Independent online learning hours 20.00 Private study hours 100.00 Total Contact hours 30.00 Total hours (100hr per 10 credits) 150.00

### Private study

Private study consists of 3 hours of review of the lecture/tutorial materials per week (total 30 hours), 20 hours of review for the final exam, and 50 hours for each of the two coursework assessments.

### Opportunities for Formative Feedback

Attendance and formative coursework.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Coursework 1 10.00 In-course Assessment Coursework 2 10.00 Total percentage (Assessment Coursework) 20.00

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

Exams
 Exam type Exam duration % of formal assessment Online Time-Limited assessment 2 hr 80.00 Total percentage (Assessment Exams) 80.00

This module will be reassessed by an online time-limited assessment.