Nystrom implementation of a combined field integral equation using approximate helmholtz decompositioncs of the current on a PEC

Surface integral equations (SIE) are extensively used in solving electromagnetic field radiation and scattering problems. The electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) are the two fundamental surface integral equations used for perfect electric conductor (PEC) objects. MFIE has a better conditioned system matrix compared to the EFIE. However, the EFIE can be applied to a wider range of structures including open structures and structures with geometric singularities. On the other hand, EFIE suffers from a low-frequency breakdown. A common disadvantage of EFIE and MFIE is the interior resonance problem for closed surfaces. The problem can be remedied by applying combined field integral equation (CFIE) which is a linear combination of EFIE and MFIE. Furthermore, CFIE provides a better conditioning than both EFIE and MFIE. However, the low-frequency breakdown inherited from EFIE still exists in CFIE. Recently, EFIE-hd has been proposed, which is an EFIE-based formulation that relies on global surface integral constraints to enforce an approximate Helmholtz decomposition (HD) of the current. It has been demonstrated that the low-frequency breakdown of the EFIE is alleviated by the EFIE-hd.