Advances in broadband and time-domain fast multipole research

The Multilevel Fast Multipole Method (MLFMA) allows to solve boundary integral equations involving several millions of unknowns. In this presentation some advanced MLFMA techniques in time and frequency domain will be discussed. First, attention will be devoted to a new broadband technique allowing to extend the classical technique to the low frequencies. Next, we will turn to the time-domain version of the MLFMA and show how the Calderón identities can used to obtain a much more efficient preconditioning. Finally, an asynchronous parallelization strategy for the MLFMA will be outlined. The obtained results will be illustrated by a collection of numerical results, both in 2D and in 3D.