A 2D Chebyshev differential operator for the elastic wave equation Original Research Article

This work analyses the performance of a two-dimensional Chebyshev differential operator for solving the elastic wave equation. The technique allows the implementation of non-periodic boundary conditions at the four boundaries of the numerical mesh, which requires a special treatment of these conditions based on one-dimensional characteristics. In addition, spatial grid adaptation by appropriate one-dimensional coordinate mappings allows a more accurate modeling of complex media, and reduction of the computational cost by controlling the minium grid spacing. The examples illustrate the ability of the method to simulate Rayleigh waves around a corner and adapt the mesh to the model geometry. In addition, a domain decomposition example shows how the boundary treatment handles wave propagation from one mesh to another mesh.