THE WAVE-EQUATION IN GENERALIZED COORDINATES

This work introduces a spectral collocation scheme for the viscoelasti c wave equation transformed from Cartesian to generalized coordinates. Both the spatial derivatives of field variables and the metrics of th e transformation are calculated by the Chebychev pseudospectral method . The technique requires a special treatment of the boundary condition s, which is based on 1-D characteristics normal to the boundaries. The numerical solution of Lamb's problem requires two 1-D stretching tran sformations for each Cartesian direction. The results show excellent a greement between the elastic numerical and analytical solutions, demon strating the effectiveness of the differential operator and boundary t reatment. Another example, requiring 1-D transformations, tests the pr opagation of a Rayleigh wave around a corner of the numerical mesh. Tw o-dimensional transformations adapt the grid to topographic features: a syncline, and an anticlinal structure formed with fine layers.