Experiments on Iterative Methods and the Fast Multipole Method in Electromagnetic Scattering Calculations

We describe the iterative solution of dense linear systems arising from a surface integral equation of electromagnetic scattering. The complex symmetric version of QMR has been used as an iterative solver together with a sparse approximate inverse preconditioner. The preconditioner is computed using the topological information from the computational mesh. The matrix-vector products are computed with the multilevel fast multipole method. The iterative solver is faster than the direct LU factorization of the matrix starting from less than a thousand unknowns. The fast multipole method becomes faster than the direct way of computing the matrix-vector product starting from a few thousand unknowns. The fast multipole method makes it possible to solve of dense linear systems of hundreds of thousands of unknowns because the coeecient matrix is not formed explicitly, which results in huge memory savings.