Preconditioned Electric Field Integral Equation Based On Calderón Formulas For Three-dimensional Electromagnetic Scattering

Calderón multiplicative preconditioner can improve the spectrum property of electric fieldintegral operator and converge rapidly. This proposed preconditioner is applicable to open andclosed structures, straightforward to implement, and can easily avoid the breakdown for method ofmoments(MoM) at low frequence. Calderón multiplicative preconditioner uses RWG and BC basisfunctions to discretize electric field integral operator, which avoids the singularity of Gram matrix,and is trivially integrated into existing MoM codes.At first, the surface integral equations, including electric field integral equation, magnetic filedintegral equation and combined field integral equation, are constructed. The basic theory and majorsteps of the method of moments are described, and the spectrum property of electric field integralequation is introduced. Then the Calderón identity is constructed, which combined the electric fieldintegral operator and the magnetic field integral operator. Because RWG and BC basis functions areneeded to discretize integral operator, this paper uses node-line-patch method to connect two basisfunctions rapidly, and constructs the transformational expressions of two basis functions. In order toreduce the massive storage made by Calderón multiplicative preconditioner interfaced with MoM,adaptive integral method is introduced to reduce the storage and speed up the multiplication ofmatrix and vector. At last, the validity of Calderón multiplicative preconditioner is verified. Andnumerical results demonstrate that the EFIE system obtained using the Calderón multiplicativepreconditioner converges rapidly, independently of the discretization density.