A symmetric FEM-IE formulation with a single-level IE-QR algorithm for solving electromagnetic radiation and scattering problems

This paper presents, for the first time in the engineering community, a symmetric coupling between the finite element and integral equation methods (FEM-IE) for solving three-dimensional unbounded radiation and scattering problems. The proposed FEM-IE is based on the E-field vector Helmholtz equation. Curl-conforming vector finite elements are used to discretize the interior region, whereas the divergence-conforming surface elements are utilized in the IE truncation surface. The symmetry in the IE part is restored through the application of the Calderon-projector. Moreover, the IE computations are accelerated using a single level QR algorithm. This reduces both memory and computational time. Furthermore it allows the use of different Green´s functions for the exterior problem, with only minor modifications on the algorithm. The resulted system of equations is solved with a very efficient preconditioned conjugate gradient (PCCG) with a p-Multiplicative Schwarz preconditioner.