CSPlib: A performance portable parallel software toolkit for analyzing complex kinetic mechanisms

Computational singular perturbation (CSP) is a method to analyze dynamical systems. It targets the decoupling of fast and slow dynamics using an alternate linear expansion of the right-hand side of the governing equations based on eigenanalysis of the associated Jacobian matrix. This representation facilitates diagnostic analysis, detection and control of stiffness, and the development of simplified models. We have implemented CSP in a C++ open-source library CSPlib using the Kokkos parallel programming model to address portability across diverse heterogeneous computing platforms, i.e., multi/many-core CPUs and GPUs. We describe the CSPlib implementation and present its computational performance across different computing platforms using several test problems. Specifically, we test the CSPlib performance for a constant pressure ignition reactor model on different architectures, including IBM Power 9, Intel Xeon Skylake, and NVIDIA V100 GPU. The size of the chemical kinetic mechanism is varied in these tests. As expected, the Jacobian matrix evaluation, the eigensolution of the Jacobian matrix, and matrix inversion are the most expensive computational tasks. When considering the higher throughput characteristic of GPUs, GPUs performs better for small matrices with higher occupancy rate. CPUs gain more advantages from the higher performance of well-tuned and optimized linear algebra libraries such as OpenBLAS.

计算奇异摄动法（Computational singular perturbation, CSP）是一种用于分析动力系统的方法。其通过基于关联雅可比矩阵（Jacobian matrix）的特征分析，对控制方程的右端项开展交替线性展开，以此实现快慢动力学的解耦。该表征方式可辅助开展诊断分析、刚性检测与控制，以及简化模型的构建。我们基于Kokkos并行编程模型，在C++开源库CSPlib中实现了CSP方法，以实现跨多样异构计算平台的可移植性，涵盖多核/众核CPU与图形处理器（GPU）。本文详细阐述了CSPlib的实现方案，并通过多组测试算例展示了其在不同计算平台上的计算性能。具体而言，我们针对恒压点火反应器模型，在包括IBM Power 9、英特尔至强Skylake处理器以及NVIDIA V100 GPU在内的多种架构上测试了CSPlib的性能。在上述测试中，化学动力学机理的规模被设置为不同取值。正如预期，雅可比矩阵求值、雅可比矩阵特征求解以及矩阵求逆是计算开销最高的三类任务。考虑到GPU的高吞吐特性，在占用率较高的小矩阵场景中，GPU表现更优；而CPU则可依托经过良好调优与优化的线性代数库（如OpenBLAS）获得更显著的性能优势。