Fast direct (noniterative) solvers for integral-equation formulations of scattering problems

For problems involving resonant or near-resonant structures, what is needed is a direct (noniterative) solver with reduced computational complexity. A family of such solvers are introduced. In addition to being alternatives to iterative solvers, fast direct solvers can also be used in the framework of iterative solvers as a preconditioner and to obtain accurate initial guess for parts of the geometry. In both cases, the objective is to utilize the direct solvers in a way to accelerate the iterative solvers by reducing the number of iterations required to required to reach the given convergence criteria. The fast direct solvers presented in this paper are based on the recursive interaction matrix algorithm (RIMA) and exploit the aggregation concept of the recursive aggregate T-matrix algorithm (RATMA) to accelerate the solution.