论文标题
超级交易：高维偏微分方程的高效，无基质的有限元库
hyper.deal: An efficient, matrix-free finite-element library for high-dimensional partial differential equations
论文作者
论文摘要
这项工作介绍了具有高阶不连续的Galerkin方法的有效，无基质的有限元库Hyper.Shiper.ther。它建立在低维有限元库Deal.ii上，以创建复杂的低维网格并单独操作它们。这些网格通过即时张量产品组合在一起，库提供了新的特殊用途高度优化的无矩阵功能来利用域分解以及通过MPI-3.0功能共享内存。节点级的性能分析和对多达147,456个CPU核心的强/弱规模研究证实了实施的效率。据报道，在高度的6D相空间中，据报道了高维对对流问题的高维度和vlasov- poisson方程的结果。
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.
