A Preconditioning Strategy for the Mortar Element Electric Field Integral Equation

International audienceThe scattering of time-harmonic waves by perfect electrical conductors can be modelled by boundary integral equations. The EFIE in particular is a flexible and accurate modelling tool: it can be applied to open and closed scatterers, it allows for the incorporation of a surface impedance as a means to model conductive loss, and it is known to provide accurate results. In recent years, the use of the EFIE to model scattering phenomena has been demonstrated on increasingly complex scatterers. The combination of acceleration by the MLFMA and scalable and asynchronous parallelization of the algorithm have enabled to application of the EFIE on examples involving hundreds of millions of unknowns. In these algorithms, however, the geometry handling is still done sequentially. The geometry is stored in a single data structure that is loaded from disk and processed by each process. This remaining sequential portion of the algorithm will limit the further increase in the size of problems that can be tackled. In cite myself, a mortar element method for the EFIE has been introduced. Is has been shown that this method allows for the separate preprocessing and storage of different parts of the geometry. In this contribution, it is shown how the resulting saddle point system can be solved iteratively by application of a suitable preconditioner. The electrodynamical part of the system matrix is preconditioned using an extension of the Calderon preconditioner introduced in cite Nedelec. The resulting spectrum of the saddle point system is further optimised by devising and applying a preconditioner for the Schur complement of the electrodynamical component. The saddle point formulation of the EFIE is revisited, the discretization and preconditioning schemes are specified, and results that proof the effectiveness of the method are presented