ИСТИНА

1. Calculation of matrix elements for boundary integral equations in 2D grating diffraction problems is the most time-consuming stage of the computation. We discuss properties and methods of computation of the grating Green function (Quasiperiodic fundamental solution of the Helmholtz equation). 2. A version of Galerkin finite element discretization of BIE on polygons involves convolutions of a kernel with logarithmic singularity and Legendre polynomials. A formula for matrix elements of Bessel-type potentials in the basis of Legendre polynomials is presented; its relationship to hypergeometric identities, generalizations (relevant and irrelevant to the numerical algorithm), and computational aspects are discussed.