Расширение области применимости спектрального метода граничных интегральных уравнений для решения задач фотоники

Abstract

The work is devoted to the modern extension of classical method, that for a long time was not applicable to study state-of-art problems, while it provides fast and accurate solution. With this method electromagnetic transmission problem for Helmholtz equation is reformulated in terms of boundary integral equations (BIE). By means of parameterization BIE are reduced to those over a circle. It permits the singularity subtraction to calculate integrals numerically by using the simplest quadrature rules. The use of Fast Fourier Transform (FFT) which is based on trapezoidal rule gives rise to speed up calculations. With modern extension by conformal mapping approach not only ellipsoidal shapes but also other smooth closed boundaries and even polygonal shapes are amenable to investigation