Fast Multipole Methods and Microlocal Discretisation for Solving Integral Equations in Electromagnetism

Within the solution of integral equations of scattering problems, in order to deal with the well-known high frequency problem, we suggest a coupling of two kind of methods. A microlocal discretisation method enables one to reduce efficiently the size of the system considering an approximation of the phase function of the unknown. However, the method needs an expensive precalculation. We then use the fast multipole method in order to speed up this precalculation. The coupling has been very satisfying within an application to the Després's integral equations for acoustic and electromagnetic problems.