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

求解偏微分方程（PDE）的数值方法在许多应用领域都具有核心意义。不断增加的模型细节几乎需要无限的计算机能力。为了有效地利用现代硬件，需要新的专用数值方法。不断增长的并行性，特别是指令级并行性，以及内存和计算速度之间日益增长的差距，给计算机系统带来了特殊的挑战。这一建议的目的是提高一类广泛的数值方法的硬件效率安装偏微分方程。通过在当前硬件限制下开发现代数值方法，我们将提供易于适用于现有仿真代码的方法。数值方法是基于块状krylov方法的初步工作。将它们与实时并行方法相结合，可以方便地透明地使用现代cpu的矢量单元，从而可以利用可达到的峰值性能的很大一部分。该方法允许经典低阶方法无法实现的加速，并且进一步增加了局部问题的大小，有助于改进强尺度。我们将通过开发新的数值方法、分析它们的性能、高效的硬件实现和验证来提高硬件效率。

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.