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

国家的最先进的有限元软件库专注于使用稀疏矩阵结构的线性代数，因为它们的易用性和高效率的代数多重网格求解器的可访问性。然而，稀疏矩阵向量积的每字节存储器加载的小于一个浮点运算的低计算强度及其对现代计算机架构的后果尚未得到解决。在原型应用中，具有更高计算强度的基于张量积的无矩阵码已被证明在当前架构上具有上级优势，具有很高的未来潜力。因此，我们建议在deal.II软件库中实现完全无矩阵的基础设施，用于广泛的应用程序和高效的几何多重网格求解器。建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，以及由此产生的多重网格求解器的基准测试。该实现将成为开源软件库协议的一部分。在某种程度上，这将使数百名活跃的研究人员受益于它，而无需对他们的代码进行重大更改。

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.