Multi-domain Chebyshev-Fourier method for the solution of the equations of motion of dynamic elasticity
type: Item
instance of: scholarly article
title: Multi-domain Chebyshev-Fourier method for the solution of the equations of motion of dynamic elasticity
zbMATH Open document ID: 0769.73094
DOI: 10.1016/0021-9991(92)90241-P
author: S. Singh
published in: Journal of Computational Physics
publication date: 1992-11-23T00:00:00Z
review text: A multi-domain approach for the solution of the equations of elasticity in two spatial dimensions is presented. The equations of momentum conservation and the stress-strain relations are recast as a system of five coupled equations in which the particle velocities and the stresses are the unknowns. Solution schemes for \(2D\) both Cartesian and polar coordinates are derived. In both cases the solution is assumed to be periodic in one coordinate (\(X\) or \(\theta\) direction) and nonperiodic in other direction. The numerical algorithm uses a Fourier expansion in the periodic direction and domain decomposition and a modified Chebyshev expansion in the remaining direction. The multi-domain approach is tested against problems with known solutions. In all cases it appears as accurate as solutions with a single domain. The multi-domain concept adds flexibility and improves efficiency. It allows use of different grid sizes in different regions depending on the material properties and allows a relatively uniform grid spacing in the case of polar coordinates.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 74B99
zbMATH DE Number: 69667
zbMATH Keywords: \(2D\) Cartesian and polar coordinates
zbMATH Keywords: momentum conservation
zbMATH Keywords: stress- strain relations
zbMATH Keywords: Fourier expansion
zbMATH Keywords: periodic direction
zbMATH Keywords: domain decomposition
zbMATH Keywords: modified Chebyshev expansion
reviewed by: Ladislav Prášek
MaRDI profile type: Publication
cites work: Q4039908
cites work: On Numerical Boundary Treatment of Hyperbolic Systems for Finite Difference and Finite Element Methods
cites work: Absorbing boundaries for wave propagation problems
description: scientific article; zbMATH DE number 69667