Accurate hybrid techniques for the method of moments in 2D

The integral equations of high frequency electromagnetic scattering can be solved numerically by means of the method of moments. Higher order basis functions such as B-splines is a means to improve the accuracy.For smooth convex scatterers and high frequencies the oscillatory behaviour of the solution makes it possible to obtain sparse matrices, and some speedup, through modification of the integration path in the integral equation. This is straightforward for the two-dimensional TM case.In order to increase sparsity and handle the standing waves that are prominent for the TE case, the shadow region can be treated separately, in a hybrid scheme based on a priory knowledge about the solution. An accurate method to combine solutions in this hybrid scheme is presented. The hybrid technique reduces the number of basis functions drastically but high accuracy and sparsity are not fully compatible.