Virtual Event: Annual Seminar 2020

The discontinuous Galerkin (DG) method is, by now, a well established numerical method
in nearly all areas of computational and geophysical fluid dynamics. In addition to the
ability to use high-order approximation spaces, its robustness for problems with shocks
and discontinuities and its natural support for h- and p-adaptivity count as the main
strengths. However, a persistent issue of DG discretizations is a high demand for
computational resources which can only be partially offset by efficient parallel scaling.
In this work, we present a new quadrature-free discontinuous Galerkin formulation for the
nonlinear shallow-water equations (SWE), that replaces quadrature integrations by
analytical evaluations. The method is implemented within the ExaStencils code generation
framework. We describe the whole code generation pipeline starting with the mapping of
the new formulation of the SWE to our Python frontend GHODDESS through to an
optimized stand-alone C++ code. Using automatically generated block-structured grids, we
exploit performance benefits over unstructured grids while still being flexible enough to
sufficiently capture the coastal geometry.