New preconditioning methods based on Calderón´s formulae for PMCHWT formulation

Preconditioning methods based on Calderón´s formulae for PMCHWT formulations for Maxwell´s equations in 3D are discussed. We propose two preconditioning methods which use different basis functions for surface electric and magnetic currents. The first method is a preconditioning just by appropriately ordering the coefficient matrix and using the Grammian matrix as the preconditioner. The second type utilises preconditioners constructed by using matrices needed in the main FMM algorithms. We will show through several numerical examples that these two preconditioning methods are faster than conventional methods.