A natural way to solve a large problem is to subdivide it into a collection of smaller problems. In computational mathematics that falls under the general umbrella of domain decomposition methods or subspace correction methods. Given that the smaller problems may be solved on different computational grids or even different function spaces, the tricky part of the procedure is combining the information to get a solution to the original problem. These techniques are of interest in areas as diverse as parallel programming, where we want to solve the problem on each sub-domain as independently as possible, to multiscale physics where various aspects of the model may be defined on different time scales.
A possible application area for this project is Stellar Astronomy. The project will involve both computational and mathematics aspects, but the focus will depend on the student's interest.