Application of the difference Gaussian rules to solution of hyperbolic problems
Two of the authors earlier suggested a method of calculation special grid steps for three point finite-difference scheme which yielded exponential superconvergence of the Neumann-to-Dirichlet map [cf. \textit{V. Druskin} and \textit{L.Knizhnerman}, SIAM J. Numer. Anal. 37, No. 2, 403-422 (2000; Zbl 0947.65127)]. This approach to solve the two-dimensional time-domain wave problem and 2.5-D elasticity system in cylindrical coordinates is applied. The numerical experiments exhibit exponential convergence at prescribed points, with the cost per grid node close to that of the standard second order finite-difference scheme. The scheme demonsrates high accuracy with slightly more than two grid point per wavelength. The reduction of the grid size by one order compared to the standard scheme with the equidistant grids is observed.
scientific article; zbMATH DE number 1437289