ExaDG - High-order discontinuous Galerkin for the exa-scale

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State-of-the-art finite-element software libraries focus on using sparse-matrix structures for their linear algebra because of their ease of use and the accessibility of highly efficient algebraic multigrid solvers. Nevertheless, the low computational intensity of less than one floating point operation per byte of memory loaded of the sparse matrix vector product and its consequences on modern computer architectures have not been addressed. In prototypical applications, tensor product based matrix-free codes with much higher computational intensity have proven superior on current architectures with high potential for the future. Therefore, we propose to implement full matrix-free infrastructure for wide ranges of applications and efficient geometric multigrid solvers in the deal.II software library. The proposed work encompasses efficient multi--threaded implementation of local operations, embedding into the existing message passing environment, and the benchmarking of the resulting multigrid solvers. The implementation will become part of the open source software library deal.II in a way, that will allow hundreds of active researchers to benefit from it without major changes in their code.