Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation

• A numerical dispersion analysis for the linear elastodynamics equations is performed.
• The numerical approximation is carried out with NURBS-based Isogeometric Analysis.
• Anisotropic curves and errors of compressional and shear wave velocities are provided.
• The dispersion analysis is compared for B-splines and NURBS of different regularity.

In this paper, we carry out a numerical dispersion analysis for the linear two-dimensional elastodynamics equations approximated by means of NURBS-based Isogeometric Analysis in the framework of the Galerkin method; specifically, we consider the analysis of harmonic plane waves in an isotropic and homogeneous elastic medium. We compare and discuss the errors associated with the compressional and shear wave velocities and we provide the anisotropic curves for numerical approximations obtained by considering B-spline and NURBS basis functions of different regularity, namely globally C0C0- and Cp−1Cp−1-continuous, pp being the polynomial degree. We conclude our analysis by numerically simulating the seismic wave propagation in a sinusoidal shaped valley with discontinuous elastic parameters across an internal interface.