High-accuracy finite-difference schemes for solving elastodynamic   problems in curvilinear coordinates within multiblock approach
  We propose highly accurate finite-difference schemes for simulating wave propagation problems described by linear second-order hyperbolic equations. The schemes are based on the summation by parts (SBP) approach modified for applications with violation of input data smoothness. In particular, we derive and implement stable schemes for solving elastodynamic anisotropic problems described by the Navier wave equation in complex geometry. To enhance potential of the method, we use a general type of coordinate transformation and multiblock grids. We also show that the conventional spectral element method (SEM) can be treated as the multiblock finite-difference method whose blocks are the SEM cells with SBP operators on GLL grid. 
Leonid Dovgilovich and Ivan Sofronov
math.NA