On sparsity related to the integral equations of 2D electromagnetic scattering

The integral equations of electromagnetic scattering are often solved with the Fast Multipole Method. If the application involves multiple excitations one could instead consider methods that separate factorization and solution. The cost of an elaborate factorization could then be compensated for by an efficient solution. An approach to obtain substantial sparsity in the solution step is considered here. By using the generality provided by the integral representation, the kernel is modified so as to create sparsity in the resulting linear system. In the two modifications that are described here there is an attempt to optimize the shape of the kernel with respect to sparsity and accuracy.