Solving elastodynamics in a fluid–solid heterogeneous sphere: a parallel spectral element approximation on non-conforming grids

We present a spectral element approach for modeling elastic wave propagation in a solid–fluid sphere where the local effects of gravity are taken into account. The equations are discretized in terms of the displacement in the solid and the velocity potential in a neutrally stratified fluid. The spatial approximation is based upon a spherical mesh of hexahedra in which local refinement allows for adapting the discretization to the variation of elastic parameters in both the solid and the fluid regions. Continuity constraints across the non-conforming interfaces are introduced through Lagrange multipliers which are further discretized by the mortar element method. Due to the spherical nature of the non-conforming interfaces the mortar method turns out to be functionally conforming and allows for an equal-order interpolation of the primal variables and the Lagrange multipliers. The method is shown to provide an accurate solution when compared to analytical calculations obtained for radial models of elastic parameters. Its parallel implementation is based upon a simple domain decomposition strategy which makes it efficient to solve large problems as those imposed by planetary scales.