A novel, high-order, parallel-in-time integration procedure for complex fluid flows

一种用于复杂流体流动的新颖、高阶、时间并行积分程序

• 批准号: 457811052
• 负责人: Dr. Jonas Zeifang
• 金额: --
• 依托单位: Mathematics and Statistics
• 依托单位国家: 德国
• 项目类别: WBP Fellowship
• 财政年份: 2021
• 资助国家: 德国
• 起止时间: 2020-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/457811052?language=en
• 关键词: novel; order; parallel; time; integration

In this project, the class of implicit multiderivative (MD) schemes for numerical treatment of ordinary differential equations is analyzed, extended and used as a parallel-in-time integrator for complex partial differential equations. Yielding high-order of accuracy with relatively low storage requirements, MD schemes offer a highly attractive option for being combined with a spatial discretization by discontinuous Galerkin spectral elements (DGSEM). A subset of the class of MD schemes, written in predictor/corrector form, provides a natural possibility of time parallelization, being of course attractive for high performance computing.The first step in this project is the analysis and development of novel MD schemes with a special focus on memory requirements, discretization error and temporal adaptivity. Having those schemes in place, they are combined with the DGSEM. Here, focus is on a consistent discretization of the multiderivative terms being essential for a stable method as well as on the exploitation of the nodal structure of the DGSEM. Finally, the time-parallel capabilities of MD schemes are investigated. As the implementation is done within a spatially parallelized code framework suitable for high performance computing, not only analytical investigations are carried out but also practical questions on real-world examples can be tackled.

在这个项目中，隐式多导数（MD）格式的数值处理常微分方程的类进行了分析，扩展，并作为一个并行的时间积分复杂的偏微分方程。MD方案以相对较低的存储要求获得高精度，提供了一个非常有吸引力的选择，可以与不连续Galerkin谱元素（DGSEM）的空间离散相结合。一类MD计划的一个子集，写在预测器/校正形式，提供了一个自然的可能性的时间并行化，当然是有吸引力的高性能computing.The第一步，在这个项目是分析和开发新的MD计划，特别注重内存需求，离散化误差和时间自适应性。这些计划到位后，它们与DGSEM相结合。在这里，重点是一致的离散化的多导数项是必不可少的一个稳定的方法，以及开发的节点结构的DGSEM。最后，研究了MD格式的时间并行能力。由于实现是在一个空间并行代码框架内进行的，适用于高性能计算，不仅进行了分析研究，而且可以解决现实世界中的实际问题的例子。