Hardiman/IRCSET Research Scholarships

Numerical Analysis: algorithm design, theory, implementation and application.

NUI Galway is offering fully-funded, four-year PhD scholarships. The scholarships provide for fees and a stipend of € 16,000 per year. Enrolment is expected in September 2012. For full details on the application procedure, please see http://www.nuigalway.ie/hardiman-scholarships. The deadline for applications is Saturday, 7^th January, 2012.

In addition, the Irish Research Council for Science, Engineering and Technology (IRCSET) funds three-year PhD scholarships, providing for fees, and a stipend of €16,000 per year, and some expenses for conference travel and computer equipment. For full details on the application procedure, please see http://www.ircset.ie/tabid/63/default.aspx. The deadline is Wednesday, 15^th of February, 2012. However, interested students should begin the application process several weeks before that.

I am interested in supervising a PhD in the area of numerical analysis, particularly in designing schemes for solving differential equations and linear systems of equations.

Project details

What is it about?

Many mathematical models are presented in the form of a differential equation. To get useful information from the model, we mush be able to solve the differential equation. Usually, it is not possible to do that exactly, so we have to use numerical scheme to generate approximate solutions.

However, it is not enough to design a suitable method: one also must

devise a mathematical analysis to prove that it gives a useful solution;
Implement the method in order to solve the problem.

The types of problems I am interested in most often arise in modelling fluid flow. We use Finite Element and Finite Difference methods. To implement these, one must be able to solve very large systems of equations (thousands of variables, maybe millions). So I'm also interest in methods for solving very large systems of equations.

What are the other buzz-words?

Singularly perturbed problems; coupled systems; boundary and interior layers; multigrid methods; direct solvers; sparse grids; boundary layers; coupled systems; domain decomposition; fast solvers...

Who should be interested?

This project is in the area of computational mathematics. The idea candidate would have a primary degree or Masters in Mathematics, or a closely related discipline, with an interest in linear algebra and differential equations, and some experience of programming.

Why consider this PhD project?

This is a rapidly developing area of numerical analysis and scientific computing. It presents a huge array of fascinating open problems. On completion, a graduate would be well placed to seek postdoctoral experience in both theoretical and application driven fields, as well as industry positions with significant scientific computing demands.

How do I apply?

First you could contact me directly do discuss the project. You should also look at the schemes terms and conditions, particularly the eligibility criteria, and the application procedure.