New trends in frequency-domain surface integral equations

Surface integral equations (SIEs) are widely used to simulate and analyze electromagnetic scattering and radiation from arbitrary -shaped conducting and piecewise homogeneous penetrable structures. These methods are based on the surface equivalence principle, where the original boundary value problem for (time -harmonic) Maxwell's equations is reformulated and expressed in terms of surface -integral operators and equivalent sources. The attractive feature of this procedure is that it essentially decreases the dimensionality of the problem by one. Another great advantage of SIEbased methods is that, in unbounded regions, radiation conditions are automatically satisfied, and thus, absorbing boundary conditions or mesh truncation techniques is not needed. These nice features, however, do not come without a cost. The linear system obtained after a discretization process involves a fully populated matrix that is expensive to solve and requiring advanced fast solution strategies as the problem size increases. Special integration routines are needed to evaluate singular integrals efficiently and accurately. The underlying integral operators, equations, and the corresponding discretized linear systems may suffer from low -frequency and dense-discretization breakdowns, low -frequency cancellation, or other types of inaccuracies, as well as instabilities and ill conditioning due to resonances and extreme material parameter