Accuracy in modeling the acoustic wave equation with Chebyshev spectral finite elements

Abstract A quantitative study of dispersion in Chebyshev spectral finite element solutions to the one- and two-dimensional scalar wave equations is presented. The spectral elements employ central time differencing and three mass matrix treatments: consistent, row-summed and diagonal-scaled. The one-dimensional axisymmetric wave equation is also formulated and solved with Chebyshev spectral elements. The computationally efficient, row-summed mass matrix formulation is shown to exhibit minimal dispersion. One- and two-dimensional examples highlight the effects of dispersion.

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