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High order finite difference methods are efficient to solve wave propagation problems on smooth domains. The summation-by-parts (SBP) property discretely mimics the integration-by-parts principle and is a key ingredient to derive stable schemes. Boundary and material interfaces conditions are often imposed weakly by using a penalty technique, similar to numerical fluxes in a discontinuous Galerkin method. For wave equations in second order form, an alternative approach is SBP operators with ghost points, which provide extra degrees of freedom to strongly impose boundary and interface conditions.
The speaker will present a new method, combining SBP operators with and without ghost points, for the elastic wave equations on curvilinear meshes. The mesh sizes are determined by the velocity structure of the elastic material resulting in non-conforming grid interfaces with hanging nodes, which are numerically handled by interpolation. The overall scheme is energy-conserving and stable under essentially the same time step restriction for periodic problems. Numerical experiments will be presented to verify the stability and accuracy properties, and its robustness on benchmark problems in seismology.
This is joint work with Anders Petersson, Lawrence Livermore National Laboratory, USA and Lu Zhang, Columbia University, USA.