High-order boundary perturbation methods (Q2758022)

The paper is devoted to the method of boundary variations and analytic continuation for solving diffraction and scattering methods. This method is based on the observation that electromagnetic fields behave analytically with respect to perturbations of the scattering surface. After a short historical review on boundary perturbation methods the authors present a detailed account of their high-order boundary perturbation theory and of resulting numerical algorithms. NEWLINENEWLINENEWLINEThe methods are based on the deep results that the scattered fields are analytic in spatial and perturbation variables. This justifies recursive formulas for their Taylor series representation. Since the convergence radius of the Taylor series may be small, the authors propose different methods for the analytic continuation of the series beyond its disk of convergence. Numerical results confirm that high-order perturbation methods can give very efficiently accurate results not attainable by other methods.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00050].