A short wavelength approximation of a boundary integral operator for two-dimensional isotropic and homogeneous elastic bodies is derived from first principles starting from the Navier-Cauchy equation. Trace formulas for elastodynamics are deduced connecting the eigenfrequency spectrum of an elastic body to the set of periodic rays where mode conversion enters as a dynamical feature.

We study the effect of approximation matrices to semi-discrete relaxation schemes for the equations of one-dimensional elastodynamics. We consider a semi-discrete relaxation scheme and establish convergence using the Lp theory of compensated compactness. Then we study the convergence of an associated relaxation-diffusion system, inspired by the scheme. Numerical comparisons of fully-discrete sc...

This paper completes a preceeding paper on the algebraic formulation of elastostatics [Tonti, Zarantonello (2009)]. It shows how to obtain a numerical formulation for elastodynamics by avoiding any process of discretization of differential equations, i.e. PDE-free formulation. To this end, we must analyse in more detail the discretization of time by highlighting the need to introduce a dual sub...

We present an adaptive spacetime discontinuous Galerkin (SDG) method for linearized elastodynamics. The SDG method uses a simple Bubnov-Galerkin projection that delivers stable and oscillation–free solutions, with O (N) complexity and exact momentum balance on every spacetime element. An extended version of the Tent Pitcher algorithm generates unstructured spacetime grids that support simultane...

We report the observation of Brillouin backscattering in a 50-cm long spiral high-index doped silica chip waveguide and measured frequency shift 16 GHz which is very good agreement with theoretical predictions numerical simulations based on elastodynamics equation. © 2023.