BlockXT – Block methods to transparently accelerate and vectorise time dependent simulations

求解偏微分方程组(PDE)的数值方法在许多应用领域都具有重要意义。不断增加的型号细节需要几乎无限的计算机能力。为了有效地使用现代硬件，需要新的专用数值方法。日益增长的并行度，特别是指令级并行度，以及内存和计算速度之间日益扩大的差距，给计算带来了特殊的挑战。这项建议的目的是提高一大类数值方法的硬件效率。通过在现有硬件的约束下发展现代数值方法，我们将提供易于适用于现有模拟代码的方法。数值方法是基于块Krylov方法的前期工作。将它们与时间并行方法相结合，便于透明地使用现代CPU的矢量单元，从而允许利用可达到的峰值性能的很大一部分。这种方法允许加速，这是传统低阶方法不可能实现的，并且进一步增加了局部问题的大小，有助于改进强伸缩性。我们将通过开发新的数值方法，分析它们的性能，*硬件效率的实现和*它的验证，来为*提高硬件效率做出贡献。

Numerical methods for solving partial differential equations (PDE) are of central importance in many fields of application. Constantly increasing model details require almost unlimited computer power. To use modern hardware efficiently new dedicated numerical methods are necessary. Special challenges are posed by the increasing parallelism, especially the instruction level parallelism, as well as the ever increasing gap between memory and computing speed. The aim of this proposal is improve the hardware efficiency of a broad class of numerical methods for instationary PDEs. By developing modern numerical methods under the constraints posed by current hardware, we will provide approaches which are easily applicable to existing simulation codes. The numerical approach is based on preliminary work on block-Krylov methods. Combining them with parallel-in-time methods facilitates the transparent use of vector units of modern CPUs and by this allows to utilize a significant portion of the attainable peak performance. The approach allows for a speedup that would otherwise not be possible for classical low-order methods and does furthermore increase the local problem size, contributing to an improved strong-scaling. We will contribute to * an improved hardware efficiency by * development of new numerical methods, * analysis of their performance, * a hardware-efficient implementation and * its validation.