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The shallow water equations (SWE) are a commonly used model to studytsunamis, tides, and coastal ocean circulation. However, there exist variousapproaches to discretize and solve them efficiently. Which of them is best fora certain scenario is often not known and, in addition, depends heavily on theused HPC platform. From a simulation software perspective, this places apremium on the ability to adapt easily to different numerical methods andhardware architectures. One solution to this problem is to apply codegeneration techniques and to express methods and specific hardware-dependentimplementations on different levels of abstraction. This allows for aseparation of concerns and makes it possible, e.g., to exchange thediscretization scheme without having to rewrite all low-level optimizedroutines manually. In this paper, we show how code for an advancedquadrature-free discontinuous Galerkin (DG) discretized shallow water equationsolver can be generated. Here, we follow the multi-layered approach from theExaStencils project that starts from the continuous problem formulation, movesto the discrete scheme, spells out the numerical algorithms, and, finally, mapsto a representation that can be transformed to a distributed memory parallelimplementation by our in-house Scala-based source-to-source compiler. Ourcontributions include: A new quadrature-free discontinuous Galerkinformulation, an extension of the class of supported computational grids, and anextension of our toolchain allowing to evaluate discrete integrals stemmingfrom the DG discretization implemented in Python. As first results we presentthe whole toolchain and also demonstrate the convergence of our method forhigher order DG discretizations.

Towards whole program generation of quadrature-free discontinuous Galerkin methods for the shallow water equations