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

BlockXT – 透明地加速和矢量化时间相关仿真的块方法

• 批准号: 504505951
• 负责人: Professor Dr. Christian Engwer
• 金额: --
• 依托单位: Section de Mathématiques
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/504505951?language=en
• 关键词: BlockXT; Block; methods; transparently; accelerate

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.

求解偏微分方程的数值方法在许多应用领域中具有重要意义。不断增加的模型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，新的专用数值方法是必要的。特别的挑战是由不断增加的并行性，特别是指令级并行性，以及不断增加的内存和计算速度之间的差距。该建议的目的是提高硬件效率的一类广泛的数值方法的不稳定偏微分方程。通过发展现代数值方法的约束下，目前的硬件，我们将提供的方法，很容易适用于现有的模拟代码。数值方法是基于块Krylov方法的初步工作。将它们与时间并行方法相结合，有助于透明地使用现代CPU的向量单元，从而可以利用可达到的峰值性能的很大一部分。该方法允许加速，否则将不可能为经典的低阶方法，并进一步增加局部问题的大小，有助于改善强缩放。我们将通过 * 开发新的数值方法，* 分析其性能，* 硬件高效实现及其验证，来提高硬件效率。