Manchester Applied Mathematics and Numerical Analysis Seminars Spring 1999

March 17, 1999, 2.30 pm

Lecture Theatre OF/B9 Oddfellows Hall (Material Science)

The efficient computation of accurate approximate solutions of partial differential equations at off-mesh points

Prof. Wayne Enright, Dept. of Computer Science, Univ. of Toronto

Numerical methods for partial differential equations usually determine discrete approximations only at meshpoints. These methods are generally most effective if they are allowed to dynamically adjust the location of the mesh points to match the local behaviour of the solution. Different methods will typically generate their respective discrete approximations on incompatible meshes and it then becomes difficult to compare solutions, to evaluate the quality of a particular solution, or to visualise important properties of a solution. In this talk we will introduce a method-independent interpolation procedure which can be used to efficiently generate approximate solution values at arbitrary points in the domain of interest. The accuracy associated with this interpolation procedure is consistent with the 'meshpoint accuracy' of the underlying discrete approximations.

The procedure we develop applies to a large class of methods and problems. It uses 'local' information only and is therefore particularly suitable for implementation in a parallel or network computing environment. Numerical examples will be given for some second order problems in two and three dimensions.

For further info contact either Matthias Heil (mheil@ma.man.ac.uk), Mark Muldoon (M.Muldoon@umist.ac.uk)or the seminar secretary (Tel. 0161 275 5800).