École Nationale Supérieure de
Techniques Avancées

Abstract

The Matlab library BIEPack provides abstract implementations of numerical methods for one-dimensional Fredholm integral equations. The library has been used for academic purposes and is meant to form a basis for work on Master theses and initial stages of PhD projects. The present report outlines some extensions carried out on BIEPack. A discrete Galerkin method is developped for integral operators with smooth or weakly singular kernels defined on domains with smooth boundaries. A support with piecewise polynomial function spaces is also introduced for projection methods. The choices made throughout the procedure of construction are then analysed using a set of examples based on Laplace Dirichlet and Laplace Robin problems