A generalized solution scheme for integral equations

In this work we have presented a generalization of the standard method of moments scheme to solve integral equations. Error bounds have been derived to show that the error in using a partition of unity scheme is controlled by the local error in the approximating function. We have, shown two-dimensional examples that it may be possible to take away the burden of modeling the singular nature of the current away from the fine-ness of the discretization and lay it on the choice of the basis function. We have thereby allowed for the inclusion of as much of the physics of the problem as possible, hopefully resulting in more accurate solutions in a wide variety of cases. Some examples of implementation of the method have been presented to demonstrate the h and p convergence of the method. Implementations on more realistic problems, involving a wide variety of geometries, including a three dimensional ogive will be presented at the conference.