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.

中文翻译：

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异构计算架构上浅水方程的p自适应间断伽辽金法

自摩尔定律扁平化以来，异构计算和利用集成CPU-GPU架构已成为当前的明显趋势。在这项工作中，我们提出了针对浅水方程（SWE）的 p 自适应无求积间断伽辽金方法（DG）的数值和算法重新设计。我们的新方法将离散化的非自适应（低阶）和自适应（高阶）部分的计算相互分开。因此，我们可以重叠计算低阶和高阶 DG 解分量。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 之间的分配。研究了几种设置，包括潮汐驱动流场景中的海啸模拟原型，结果表明，在适当的设置中可以实现显着的性能改进。