On the Use of Quasi-Helmholtz Projectors for Modeling Structures With Junctions at Arbitrarily Low Frequencies

This work investigates the usage of quasi-Helmholtz projectors to cure the low frequency breakdown of the electric field integral equation (EFIE) when modeling structures containing junctions. We show that the quasi-Helmholtz projectors can still efficiently perform projection into the solenoidal and nonsolenoidal subspaces in the presence of junctions. Preconditioning strategies leveraging these projectors are capable of curing the low-frequency breakdown that severely compromises the accuracy and conditioning of the EFIE. Numerical studies validate the use of algebraic multigrid approaches for achieving fast and efficient implementation of the proposed scheme for problems with multiple junctions. The effectiveness of the scheme and its applicability to problems of industrial relevance is illustrated through a series of numerical results.