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UID:submissions.pasc-conference.org_PASC21_sess182_post118@linklings.com
SUMMARY:P07 - Quadrature-Free Discontinuous Galerkin Method for Shallow-Wa
 ter Equations
DESCRIPTION:Poster\n\nP07 - Quadrature-Free Discontinuous Galerkin Method 
 for Shallow-Water Equations\n\nFaghih-Naini\n\nThe discontinuous Galerkin 
 (DG) methods are already well-established in nearly all areas of computati
 onal and geophysical fluid dynamics. Their strengths include the ability t
 o use high-order approximation spaces, robustness for problems with shocks
  and discontinuities, natural support of h- and p-adaptivity, and many oth
 er features. However, comparatively high computational costs of DG discret
 izations can only be partially offset by efficient parallel scaling. For h
 yperbolic systems discretized in time by an explicit Runge-Kutta method, t
 he most computationally expensive parts of a DG algorithm are the element 
 and edge integrals computed via loops over quadrature points. We present a
  new quadrature-free DG formulation for the nonlinear shallow-water equati
 ons that replaces quadrature integrations by analytical evaluations. In or
 der to be able to employ the quadrature-free methodology to operators with
  fraction-type nonlinearities, we propose a mixed (re-)formulation of the 
 equation system. The numerical scheme has been successfully implemented wi
 thin the ExaStencils code generation framework using a specialized Python 
 front end based on the SymPy library.
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