Multi-domain Chebyshev-Fourier method for the solution of the equations of motion of dynamic elasticity
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.
scientific article; zbMATH DE number 69667