A Chebyshev spectral element method for elastic wave modeling

The Chebyshev spectral element method which uses spectral expansion in each element,combines the ad- vantages of spectral method with those of finite element method.It provides an efficient tool in simulating elastic wave equation in complex medium.Based on weak form of elastodynamic equation,the mathematical formulations for spectral element method are presented by using Chebyshev orthogonal function.And the analytical integrate results in elastic problem with general mapping are presented using Chebyshev approach.The element by element method is introduced to reduce the memory and computation cost requiring.At last,some numerical examples are simulated to demonstrate the spectral accuracy and the efficiency in dealing with complex problem obtained by the Chebyshev spectral element method.