Space-time mesh refinement for elastodynamic equations

Overview & Synopsis

This work deals with the simulation of wave scattering in elastic, anisotropic and heterogeneous media with cracks using explicit schemes. Our goal is the development of an efficient numerical method to capture the geometrical details or the singularities of the solution in an accurate way. In the first two parts we present space-time mesh refinement methods. Adapting the time step locally to the spatial discretization allows us to diminish the CPU time and the numerical dispersion on the coarse grid. These methods are conservative, a property that ensures the stability of the numerical scheme. The cracks are taken into account using the fictitious domain method. In the third part of this work we present a new mixed finite element that ensures the convergence of this method. Finally, the last part describes the coupling between conservative space-time mesh refinement techniques and the fictitious domain method.