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

最先进的有限元软件库专注于将稀疏矩阵结构用于其线性代数，因为它们易于使用，并且可以访问高效的代数多重网格求解器。然而，稀疏矩阵向量积每个加载的存储器字节不到一个浮点运算的低计算强度及其对现代计算机体系结构的影响尚未得到解决。在典型的应用中，基于张量积的无矩阵码具有更高的计算强度，已被证明优于目前具有很大潜力的未来体系结构。因此，我们建议在Deal.II软件库中实现适用于广泛应用的全无矩阵基础设施和高效的几何多重网格求解器。拟议的工作包括高效的多线程实现本地操作，嵌入到现有的消息传递环境中，以及对产生的多网格解算器进行基准测试。这一实现将成为开放源码软件库交易的一部分。2在某种程度上，这将使数百名活跃的研究人员在不对代码进行重大修改的情况下从中受益。

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.