The mass property model and its implementation in the time-domain spectral element method

The mathematical mechanism of constructing mass property model for the time-domain spectral elements is studied in this paper. A unified mathematical method for directly deriving consistent and lumped mass matrix is established for the time-domain Chebyshev and Legendre spectral elements. The characteristics of two mass property models of the spectral elements are analyzed through comparison. Meanwhile, the rationality of mass property model of spectral element is discussed from physical perspective. This study reveals that the formation of consistent or lumped mass matrix in time-domain spectral elements depends on whether the quadrature points are coincident with the element nodes or not. To be specific, the Gauss-Legendre quadrature results in consistent mass matrix for spectral elements, and the Gauss-Lobatto quadrature leads to lumped mass matrix. The lumped mass matrix is more reasonable in physics. The two mass property models of spectral elements have comparable performance and they can both achieve good results for dynamic problems.