Reverse Operation Self-Consistent Evaluation For The Implementation Of Integral Equations Using Constant Vector Basis Functions

The integral equations (IEs) have demonstrated excellent potentials in analyzing large scale electromagnetic radiation and scattering problems. They stand out for properties like only discretization of the objects' surface, automatic satisfaction of the radiation condition, as well as no numerical dispersion. They are usually solved by the method of moment (MoM) following the Galerkin scheme. When filling the impedance matrix, special techniques for calculating the singular integrals are required. This issue may even limit our choices of the basis functions employed for the IEs. Traditionally, in electric field integral equation (EFIE), the integration by part operation is applied to avoid the hyper singular integration, which moves the gradient operator onto the testing function. But this operation, in return, requires that the basis function is div-conforming. Based on this principle, the mix-order Rao-Wilton-Glisson (RWG) function and higher order div-conforming bases are commonly adopted in literature. In this paper, the constant order basis is successfully employed to implement the EFIE. The constant vector basis function is defined in the way that each triangular element contains two orthogonal constant vectors. Instead of doing the integration by part operation, we directly evaluate the integrals from the gradient-gradient operation. The resulting hyper singularity is calculated by the reverse operation self consistent evaluation (R.O.S.E.) method. The R.O.S.E. method is based on the equivalent principle theory, which states that the corresponding equivalent currents of incident fields on an arbitrarily closed surface radiate null fields in the outside region. To keep self consistent with the original problem, we set the closed surface to coincide with the boundary of the original target. Plane waves are sampled and substituted into the equivalent equation to recover the singular terms. Afterwards, we also implement the magnetic field integral equation (MFIE) based on the constant vector basis function and combine it with the EFIE to form the internal resonance free combined field integral equation (CFIE). Various numerical tests for scattering analysis from non-penetrable targets are discussed to demonstrate the efficacy of the proposed method.