Contour Smoothing for Super-Algebraically Convergent Algorithms of 2-D Diffraction Problems

Abstract

A new method extending the scope of the superalgebraically convergent 2-D wave diffraction algorithms is proposed. The principal tool is the construction of an infinitely smooth approximation to the boundary contour. The construction is based on the ideas of Tikhonov's regularization to the stable summation of the Fourier series and the evaluation of unbounded operators. Both the algorithms for smoothing and the nonsaturated solutions for integral equations together provide the superalgebraic (faster than any algebraic) convergence. The comparison of the algorithms using the original (noninfinitely smooth) parameterization and the infinitely smooth one demonstrates the essential advantage of the latter over the former with respect to accuracy and time consumption.