异构计算架构上浅水方程的p自适应间断伽辽金方法
p-adaptive discontinuous Galerkin method for the shallow water equations on heterogeneous computing architectures
AI总结：
针对浅水方程提出一种重新设计的p自适应无求积间断伽辽金方法，通过分离并重叠低阶与高阶计算，结合自动代码生成优化CPU-GPU任务分布，在包括海啸模拟等场景中实现了显著的性能提升。
摘要：
自摩尔定律放缓以来，异构计算与利用集成CPU-GPU架构已成为明确的当前趋势。在本研究中，我们针对浅水方程（SWE），提出了一种p自适应无求积间断伽辽金方法（DG）的数值与算法重新设计。我们的新方法将离散化的非自适应（低阶）部分与自适应（高阶）部分的计算相互分离。因此，我们能够重叠低阶和高阶DG解分量的计算。此外，我们研究了主要计算内核的执行时间，并使用自动代码生成来优化它们在CPU和GPU之间的分布。研究考察了多种设置，包括在潮汐驱动流场景中的海啸模拟原型，结果表明在合适的设置下能够实现显著的性能提升。
英文摘要：
Heterogeneous computing and exploiting integrated CPU-GPU architectures has become a clear current trend since the flattening of Moore's Law. In this work, we propose a numerical and algorithmic re-design of a p-adaptive quadrature-free discontinuous Galerkin method (DG) for the shallow water equations (SWE). Our new approach separates the computations of the non-adaptive (lower-order) and adaptive (higher-order) parts of the discretization form each other. Thereby, we can overlap computations of the lower-order and the higher-order DG solution components. Furthermore, we investigate execution times of main computational kernels and use automatic code generation to optimize their distribution between the CPU and GPU. Several setups, including a prototype of a tsunami simulation in a tide-driven flow scenario, are investigated, and the results show that significant performance improvements can be achieved in suitable setups.
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