Effectiveness of boundary integral equations solution techniques

The scattering of an electromagnetic wave by a perfectly electrically conducting material is formulated by using either the electric or the magnetic field integral equations (EFIE or MFIE). When the scatterer is irradiated by an incident wave a surface current will be induced. The formulation in surface integral equations is based on the calculation of this unknown surface current. A drawback of using surface integral equations is related to the uniqueness of their solutions. In the literature several methods are introduced as a remedy. The most popular one is the combined-field integral equation (CFIE) which uses a linear combination of the MFIE and EFIE to provide a unique stable solution. A less-known method is the constrained conjugate gradient method (CCG) that minimizes a cost functional consisting of two terms. The first term is the error norm with respect to boundary integral equation, while the second term is the error norm with respect to the interior equation over a closed interior surface. In the book it is discussed the efficiency of both CCG and CFIE methods. The accuracy of the methods will be compared for closed surfaces, and at the resonant frequencies.