Application of the difference Gaussian rules to solution of hyperbolic problems
type: Item
instance of: scholarly article
title: Application of the difference Gaussian rules to solution of hyperbolic problems
zbMATH Open document ID: 0955.65063
author: Sergey Asvadurov
author: V. Druskin
author: Leonid Knizhnerman
published in: Journal of Computational Physics
publication date: 2000-08-28T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 74S20
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 1437289
zbMATH Keywords: finite-difference scheme
zbMATH Keywords: optimal grids
zbMATH Keywords: exponential superconvergence
zbMATH Keywords: hyperbolic problems
zbMATH Keywords: linear elasticity
zbMATH Keywords: wave propagation
MaRDI profile type: Publication
full work available at URL: jcph.1999.6410
OpenAlex ID: W1973189718
cites work: A Practical Guide to Pseudospectral Methods
cites work: Gaussian Spectral Rules for the Three-Point Second Differences: I. A Two-Point Positive Definite Problem in a Semi-Infinite Domain
cites work: Q4348515
DOI: 10.1006/JCPH.1999.6410
description: scientific article; zbMATH DE number 1437289