  A high-order accurate implicit-mesh discontinuous Galerkin framework for wave
propagation in single-phase and bi-phase solids is presented. The framework
belongs to the embedded-boundary techniques and its novelty regards the spatial
discretization, which enables boundary and interface conditions to be enforced
with high-order accuracy on curved embedded geometries. High-order accuracy is
achieved via high-order quadrature rules for implicitly-defined domains and
boundaries, whilst a cell-merging strategy addresses the presence of small cut
cells. The framework is used to discretize the governing equations of
elastodynamics, written using a first-order hyperbolic momentum-strain
formulation, and an exact Riemann solver is employed to compute the numerical
flux at the interface between dissimilar materials with general anisotropic
properties. The space-discretized equations are then advanced in time using
explicit high-order Runge-Kutta algorithms. Several two- and three-dimensional
numerical tests including dynamic adaptive mesh refinement are presented to
demonstrate the high-order accuracy and the capability of the method in the
elastodynamic analysis of single- and bi-phases solids containing complex
geometries.
