  This work presents the efficient, matrix-free finite-element library
hyper.deal for solving partial differential equations in two to six dimensions
with high-order discontinuous Galerkin methods. It builds upon the
low-dimensional finite-element library deal.II to create complex
low-dimensional meshes and to operate on them individually. These meshes are
combined via a tensor product on the fly and the library provides new
special-purpose highly optimized matrix-free functions exploiting domain
decomposition as well as shared memory via MPI-3.0 features. Both node-level
performance analyses and strong/weak-scaling studies on up to 147,456 CPU cores
confirm the efficiency of the implementation. Results of the library hyper.deal
are reported for high-dimensional advection problems and for the solution of
the Vlasov--Poisson equation in up to 6D phase space.
