Parallel methods for the solution of large-scale radiation and inverse scattering problems

Parallel methods and the multilevel fast multipole algorithm (MLFMA) are applied to forward- and inverse-scattering problems. A parallel MLFMA is presented that is capable of simulating electromagnetic radiation and scattering in the presence of complex media. Due to the iterative solution process and matrix-conditioning issues inherent to radiation problems, these solutions demand an effective preconditioner. A new analysis is presented to characterize the need for preconditioning, and a localized preconditioner is presented that meets this need. Reduced-rank techniques are also employed to reduce the cost of computing the preconditioner inverse.; A parallel MLFMA is also developed for 3-D, penetrable, acoustic scatterers. This is paired with the distorted-Born iterative method (DBIM) for inverse scattering. DBIM requires repeated solutions of the forward problem to compute an image. With the linear complexity offered by the MLFMA forward solver, DBIM reconstructions proceed with greatly-reduced computation. This allows the solution of very large inverse-scattering problems.