MAS3107 : Numerical and Computational Modelling

  • Module Leader(s): Prof. Patrick Briddon
  • Owning School: Mathematics & Statistics
Semesters
Semester 1 Credit Value: 10
ECTS Credits: 5.0

Aims

To introduce more advanced features of programming. Students will be able to write more complex programs in Fortran 90, making use of some advanced features for better program structure and memory management.

To introduce further techniques for numerical and computational modelling, with applications to the solution of linear systems and differential equations.

Module Summary

The speed of modern computers has opened the way to the numerical investigation of problems which are far too difficult to tackle using traditional methods. An exciting example is the problem of modelling the climate: is global warming taking place or not? Other examples range from engineering applications (the flow around aeroplane wings) to natural phenomena (the motion of the rocks deep inside the Earth, which drives the motion of the continents above). This module introduces many of the techniques necessary to solve such problems numerically, and allows you to put them into practice.

Outline Of Syllabus

More advanced programming: program structures (modules, interfaces, intents); arrays (advanced array syntax, dynamic storage allocation, assumed-shape and assumed-size arrays); subprograms (recursive functions, generic subprograms, overloading); intrinsics (advanced intrinsic functions).

Applications: finite difference methods (finite difference expressions for derivatives and the accuracy of these, dicretisation of PDEs, applications to elliptic and parabolic PDEs, forward and backward differences and the Crank-Nicolson method, stability analysis); approaches to the numerical solution of large sparse systems of linear equations (Gauss-Seidel and successive over-relaxation (SOR) methods); implementation of this formalism on a computer.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture131:0013:00Formal lectures
Guided Independent StudyAssessment preparation and completion21:002:00Class test
Guided Independent StudyAssessment preparation and completion28:0016:00Coursework/Project
Scheduled Learning And Teaching ActivitiesPractical181:0018:00Computer practicals
Scheduled Learning And Teaching ActivitiesDrop-in/surgery240:000:00Office Hours in a staff office
Guided Independent StudyIndependent study26:0012:00Revision for class test
Guided Independent StudyIndependent study13:003:00Coursework review
Guided Independent StudyIndependent study136:0036:00Studying, practising and gaining understanding of course material
Total100:00
Jointly Taught With
Code Title
MAS8107Numerical and Computational Modelling
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Practicals are used to help the students to develop their programming skills but also afford an opportunity to develop the students’ abilities at applying the theory to solving problems. Office hours provide an opportunity for more direct contact between individual students and the lecturer.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination601M25class test
Written Examination601M25class test
Exam Pairings
Module Code Module Title Semester Comment
MAS8107Numerical and Computational Modelling1N/A
Exam Pairing Resits
Module Code Module Title Comment
MAS8107Numerical and Computational ModellingN/A
Other Assessment
Description Semester When Set Percentage Comment
Written exercise1M20Project Work
Written exercise1M30Project Work
Assessment Rationale And Relationship

The project work allows the students to develop their problem solving techniques and to practise the methods learnt in the module. It also allows the assessment of the computational skills acquired by the student. The tests allow the students to assess their progress with the material. They both allow feedback to the students and so act as formative as well as summative assessment.

Reading Lists

Timetable

Disclaimer: The University will use all reasonable endeavours to deliver modules in accordance with the descriptions set out in this catalogue. Every effort has been made to ensure the accuracy of the information, however, the University reserves the right to introduce changes to the information given including the addition, withdrawal or restructuring of modules if it considers such action to be necessary.