This paper examines the application of the discontinuous Galerkin method for deformation and destruction problems of elastic and elastoplastic bodies and combined problems of elasticity and acoustics. It proposes a 2-sided crack model in the problems of destruction, an account of the elastoplastic rheology in the Prandtl-Reuss model, implementation of the dynamic contact of bodies, an algorithm for the joint solution of linear systems of acoustics and elasticity, and in particular, the issues of shelf seismic prospecting, a comparison of the responses for the model of saturated fluid and infinitely thin cracks, and a modeling of perturbations from underwater objects. The method has been implemented to find the wave picture in heterogeneous media and also the solution of deformation problems by the use of high performance computation systems.
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Miryaha et al. (2015) studied this question.
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