Using SIMD and SIMT vectorization to evaluate sparse chemical kinetic Jacobian matrices and thermochemical source terms

Accurately predicting key combustion phenomena in reactive-flow simulations, e.g., lean blow-out, extinction/ignition limits and pollutant formation, necessitates the use of detailed chemical kinetics. The large size and high levels of numerical stiffness typically present in chemical kinetic models relevant to transportation/power-generation applications make the efficient evaluation/factorization of the chemical kinetic Jacobian and thermochemical source-terms critical to the performance of reactive-flow codes. Here we investigate the performance of vectorized evaluation of constant-pressure/volume thermochemical source-term and sparse/dense chemical kinetic Jacobians using single-instruction, multiple-data (SIMD) and single-instruction, multiple thread (SIMT) paradigms. These are implemented in pyJac, an open-source, reproducible code generation platform. Selected chemical kinetic models covering the range of sizes typically used in reactive-flow simulations were used for demonstration. A new formulation of the chemical kinetic governing equations was derived and verified, resulting in Jacobian sparsities of 28.6-92.0% for the tested models. Speedups of 3.40-4.08 x were found for shallow-vectorized OpenCL source-rate evaluation compared with a parallel OpenMP code on an avx2 central processing unit (CPU), increasing to 6.63-9.44 x and 3.03-4.23 x for sparse and dense chemical kinetic Jacobian evaluation, respectively. Furthermore, the effect of data-ordering was investigated and a storage pattern specifically formulated for vectorized evaluation was proposed; as well, the effect of the constant pressure/volume assumptions and varying vector widths were studied on source-term evaluation performance. Speedups reached up to 17.60 x and 45.13 x for dense and sparse evaluation on the GPU, and up to 55.11 x and 245.63 x on the CPU over a first-order finite-difference Jacobian approach. Further, dense Jacobian evaluation was up to 19.56 x and 2.84 x times faster than a previous version of pyJac on a CPU and GPU, respectively. Finally, future directions for vectorized chemical kinetic evaluation and sparse linear-algebra techniques were discussed. (C) 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved

HPC-enabling technologies for high-fidelity combustion simulations

With the increase in computational power in the last decade and the forthcoming Exascale supercomputers, a new horizon in computational modelling and simulation is envisioned in combustion science. Considering the multiscale and multiphysics characteristics of turbulent reacting flows, combustion simulations are considered as one of the most computationally demanding applications running on cutting-edge supercomputers. Exascale computing opens new frontiers for the simulation of combustion systems as more realistic conditions can be achieved with high-fidelity methods. However, an efficient use of these computing architectures requires methodologies that can exploit all levels of parallelism. The efficient utilization of the next generation of supercomputers needs to be considered from a global perspective, that is, involving physical modelling and numerical methods with methodologies based on High-Performance Computing (HPC) and hardware architectures. This review introduces recent developments in numerical methods for large-eddy simulations (LES) and direct-numerical simulations (DNS) to simulate combustion systems, with focus on the computational performance and algorithmic capabilities. Due to the broad scope, a first section is devoted to describe the fundamentals of turbulent combustion, which is followed by a general description of state-of-the-art computational strategies for solving these problems. These applications require advanced HPC approaches to exploit modern supercomputers, which is addressed in the third section. The increasing complexity of new computing architectures, with tightly coupled CPUs and GPUs, as well as high levels of parallelism, requires new parallel models and algorithms exposing the required level of concurrency. Advances in terms of dynamic load balancing, vectorization, GPU acceleration and mesh adaptation have permitted to achieve highly-efficient combustion simulations with data-driven methods in HPC environments. Therefore, dedicated sections covering the use of high-order methods for reacting flows, integration of detailed chemistry and two-phase flows are addressed. Final remarks and directions of future work are given at the end. }The research leading to these results has received funding from the European Union’s Horizon 2020 Programme under the CoEC project, grant agreement No. 952181 and the CoE RAISE project grant agreement no. 951733.Peer ReviewedPostprint (published version

Data for pyjac-V2 paper

The data used in the creation of the the paper: "Using SIMD and SIMT vectorization to evaluate sparse chemical kinetic Jacobian matrices and thermochemical source terms" by Nicholas Curtis (UConn), Kyle Niemeyer (OSU) and Chih-Jen Sung (UConn)

GPGPU microbenchmarking for irregular application optimization

Irregular applications, such as unstructured mesh operations, do not easily map onto the typical GPU programming paradigms endorsed by GPU manufacturers, which mostly focus on maximizing concurrency for latency hiding. In this work, we show how alternative techniques focused on latency amortization can be used to control overall latency while requiring less concurrency. We used a custom-built microbenchmarking framework to test several GPU kernels and show how the GPU behaves under relevant workloads. We demonstrate that coalescing is not required for efficacious performance; an uncoalesced access pattern can achieve high bandwidth - even over 80% of the theoretical global memory bandwidth in certain circumstances. We also make other further observations on specific relevant behaviors of GPUs. We hope that this study opens the door for further investigation into techniques that can exploit latency amortization when latency hiding does not achieve sufficient performance