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.

中文翻译：

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hyper.deal：用于高维偏微分方程的高效、无矩阵的有限元库

这项工作提出了高效、无矩阵的有限元库 hyper.deal，用于使用高阶不连续伽辽金方法求解 2 到 6 维偏微分方程。它建立在低维有限元库 deal.II 之上，以创建复杂的低维网格并对其进行单独操作。这些网格通过动态张量积组合在一起，该库提供了新的专用高度优化的无矩阵函数，利用域分解以及通过 MPI-3.0 功能共享内存。对多达 147,456 个 CPU 内核的节点级性能分析和强/弱扩展研究证实了实施的效率。库超的结果。