论文信息 - Application of the Difference Gaussian Rules to Solution of Hyperbolic Problems

Application of the Difference Gaussian Rules to Solution of Hyperbolic Problems

Two of the authors earlier suggested a method of calculating special grid steps for three point finite-difference schemes which yielded exponential superconvergence of the Neumann-to-Dirichlet map. We apply this approach to solve the two-dimensional time-domain wave problem and the 2.5-D elasticity system in cylindrical coordinates. Our 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 demonstrates high accuracy with slightly more than two grid points per wavelength. The reduction of the grid size by one order compared to the standard scheme with the equidistant grids is observed.

[1] L. Knizhnerman. The simple Lanczos procedure: estimates of the error of the Gauss quadrature formula and their applications , 1996 .

[2] P. Monk,et al. Optimizing the Perfectly Matched Layer , 1998 .

[3] Vladimir Druskin,et al. Three-point finite-difference schemes, Padé and the spectral Galerkin method. I. One-sided impedance approximation , 2001, Math. Comput..

[4] Jean-Pierre Berenger,et al. A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[5] W. Rudin. Principles of mathematical analysis , 1964 .

[6] Bengt Fornberg,et al. A practical guide to pseudospectral methods: Introduction , 1996 .

[7] L. Knizhnerman,et al. Two polynomial methods of calculating functions of symmetric matrices , 1991 .

[8] Vladimir Druskin,et al. Gaussian Spectral Rules for the Three-Point Second Differences: I. A Two-Point Positive Definite Problem in a Semi-Infinite Domain , 1999, SIAM J. Numer. Anal..

[9] Irene A. Stegun,et al. Handbook of Mathematical Functions. , 1966 .

[10] B. Parlett. The Symmetric Eigenvalue Problem , 1981 .