Abstract Block-Adaptive-Tree Solar-wind Roe-type Upwind Scheme (BATSRUS), our state-of-the-art extended magnetohydrodynamic code, is the most used and one of the most resource-consuming models in the Space Weather Modeling Framework. It has always been our objective to improve its efficiency and speed with emerging techniques, such as GPU acceleration. To utilize the GPU nodes on modern supercomputers, we port BATSRUS to GPUs with the OpenACC API. Porting the code to a single GPU requires rewriting and optimizing the most used functionalities of the original code into a new solver, which accounts for around 1% of the entire program in length. To port it to multiple GPUs, we implement a new message-passing algorithm to support its unique block-adaptive grid feature. We conduct weak scaling tests on as many as 256 GPUs and find good performance. The program has 50%–60% parallel efficiency on up to 256 GPUs and up to 95% efficiency within a single node (four GPUs). Running large problems on more than one node has reduced efficiency due to hardware bottlenecks. We also demonstrate our ability to run representative magnetospheric simulations on GPUs. The performance for a single A100 GPU is about the same as 270 AMD “Rome” CPU cores (2.1 128-core nodes), and it runs 3.6 times faster than real time. The simulation can run 6.9 times faster than real time on four A100 GPUs.
more »
« less
Techniques, Tricks, and Algorithms for Efficient GPU-Based Processing of Higher Order Hyperbolic PDEs
GPU computing is expected to play an integral part in all modern Exascale supercomputers. It is also expected that higher order Godunov schemes will make up about a significant fraction of the application mix on such supercomputers. It is, therefore, very important to prepare the community of users of higher order schemes for hyperbolic PDEs for this emerging opportunity. Not every algorithm that is used in the space-time update of the solution of hyperbolic PDEs will take well to GPUs. However, we identify a small core of algorithms that take exceptionally well to GPU computing. Based on an analysis of available options, we have been able to identify weighted essentially non-oscillatory (WENO) algorithms for spatial reconstruction along with arbitrary derivative (ADER) algorithms for time extension followed by a corrector step as the winning three-part algorithmic combination. Even when a winning subset of algorithms has been identified, it is not clear that they will port seamlessly to GPUs. The low data throughput between CPU and GPU, as well as the very small cache sizes on modern GPUs, implies that we have to think through all aspects of the task of porting an application to GPUs. For that reason, this paper identifies the techniques and tricks needed for making a successful port of this very useful class of higher order algorithms to GPUs. Application codes face a further challenge—the GPU results need to be practically indistinguishable from the CPU results—in order for the legacy knowledge bases embedded in these applications codes to be preserved during the port of GPUs. This requirement often makes a complete code rewrite impossible. For that reason, it is safest to use an approach based on OpenACC directives, so that most of the code remains intact (as long as it was originally well-written). This paper is intended to be a one-stop shop for anyone seeking to make an OpenACC-based port of a higher order Godunov scheme to GPUs. We focus on three broad and high-impact areas where higher order Godunov schemes are used. The first area is computational fluid dynamics (CFD). The second is computational magnetohydrodynamics (MHD) which has an involution constraint that has to be mimetically preserved. The third is computational electrodynamics (CED) which has involution constraints and also extremely stiff source terms. Together, these three diverse uses of higher order Godunov methodology, cover many of the most important applications areas. In all three cases, we show that the optimal use of algorithms, techniques, and tricks, along with the use of OpenACC, yields superlative speedups on GPUs. As a bonus, we find a most remarkable and desirable result: some higher order schemes, with their larger operations count per zone, show better speedup than lower order schemes on GPUs. In other words, the GPU is an optimal stratagem for overcoming the higher computational complexities of higher order schemes. Several avenues for future improvement have also been identified. A scalability study is presented for a real-world application using GPUs and comparable numbers of high-end multicore CPUs. It is found that GPUs offer a substantial performance benefit over comparable number of CPUs, especially when all the methods designed in this paper are used.
more »
« less
- Award ID(s):
- 2009776
- PAR ID:
- 10466357
- Editor(s):
- Chi-Wang Shu
- Date Published:
- Journal Name:
- Communications on Applied Mathematics and Computation
- ISSN:
- 2096-6385
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Cloud microphysics is one of the most time‐consuming components in a climate model. In this study, we port the cloud microphysics parameterization in the Community Atmosphere Model (CAM), known as Parameterization of Unified Microphysics Across Scales (PUMAS), from CPU to GPU to seek a computational speedup. The directive‐based methods (OpenACC and OpenMP target offload) are determined as the best fit specifically for our development practices, which enable a single version of source code to run either on the CPU or GPU, and yield a better portability and maintainability. Their performance is first examined in a PUMAS stand‐alone kernel and the directive‐based methods can outperform a CPU node as long as there is enough computational burden on the GPU. A consistent behavior is observed when we run PUMAS on the GPU in a practical CAM simulation. A 3.6× speedup of the PUMAS execution time, including data movement between CPU and GPU, is achieved at a coarse horizontal resolution (8 NVIDIA V100 GPUs against 36 Intel Skylake CPU cores). This speedup further increases up to 5.4× at a high resolution (24 NVIDIA V100 GPUs against 108 Intel Skylake CPU cores), which highlights the fact that GPU favors larger problem size. This study demonstrates that using GPU in a CAM simulation can save noticeable computational costs even with a small portion of code being GPU‐enabled. Therefore, we are encouraged to port more parameterizations to GPU to take advantage of its computational benefit.more » « less
-
Today's high-performance computing (HPC) applications are producing vast volumes of data, which are challenging to store and transfer efficiently during the execution, such that data compression is becoming a critical technique to mitigate the storage burden and data movement cost. Huffman coding is arguably the most efficient Entropy coding algorithm in information theory, such that it could be found as a fundamental step in many modern compression algorithms such as DEFLATE. On the other hand, today's HPC applications are more and more relying on the accelerators such as GPU on supercomputers, while Huffman encoding suffers from low throughput on GPUs, resulting in a significant bottleneck in the entire data processing. In this paper, we propose and implement an efficient Huffman encoding approach based on modern GPU architectures, which addresses two key challenges: (1) how to parallelize the entire Huffman encoding algorithm, including codebook construction, and (2) how to fully utilize the high memory-bandwidth feature of modern GPU architectures. The detailed contribution is four-fold. (1) We develop an efficient parallel codebook construction on GPUs that scales effectively with the number of input symbols. (2) We propose a novel reduction based encoding scheme that can efficiently merge the codewords on GPUs. (3) We optimize the overall GPU performance by leveraging the state-of-the-art CUDA APIs such as Cooperative Groups. (4) We evaluate our Huffman encoder thoroughly using six real-world application datasets on two advanced GPUs and compare with our implemented multi-threaded Huffman encoder. Experiments show that our solution can improve the encoding throughput by up to 5.0x and 6.8x on NVIDIA RTX 5000 and V100, respectively, over the state-of-the-art GPU Huffman encoder, and by up to 3.3x over the multi-thread encoder on two 28-core Xeon Platinum 8280 CPUs.more » « less
-
null (Ed.)Error-bounded lossy compression is a state-of-the-art data reduction technique for HPC applications because it not only significantly reduces storage overhead but also can retain high fidelity for postanalysis. Because supercomputers and HPC applications are becoming heterogeneous using accelerator-based architectures, in particular GPUs, several development teams have recently released GPU versions of their lossy compressors. However, existing state-of-the-art GPU-based lossy compressors suffer from either low compression and decompression throughput or low compression quality. In this paper, we present an optimized GPU version, cuSZ, for one of the best error-bounded lossy compressors-SZ. To the best of our knowledge, cuSZ is the first error-bounded lossy compressor on GPUs for scientific data. Our contributions are fourfold. (1) We propose a dual-quantization scheme to entirely remove the data dependency in the prediction step of SZ such that this step can be performed very efficiently on GPUs. (2) We develop an efficient customized Huffman coding for the SZ compressor on GPUs. (3) We implement cuSZ using CUDA and optimize its performance by improving the utilization of GPU memory bandwidth. (4) We evaluate our cuSZ on five real-world HPC application datasets from the Scientific Data Reduction Benchmarks and compare it with other state-of-the-art methods on both CPUs and GPUs. Experiments show that our cuSZ improves SZ's compression throughput by up to 370.1x and 13.1x, respectively, over the production version running on single and multiple CPU cores, respectively, while getting the same quality ofmore » « less
-
Error-bounded lossy compression is a state-of-the-art data reduction technique for HPC applications because it not only significantly reduces storage overhead but also can retain high fidelity for postanalysis. Because supercomputers and HPC applications are becoming heterogeneous using accelerator-based architectures, in particular GPUs, several development teams have recently released GPU versions of their lossy compressors. However, existing state-of-the-art GPU-based lossy compressors suffer from either low compression and decompression throughput or low compression quality. In this paper, we present an optimized GPU version, cuSZ, for one of the best error-bounded lossy compressors-SZ. To the best of our knowledge, cuSZ is the first error-bounded lossy compressor on GPUs for scientific data. Our contributions are fourfold. (1) We propose a dual-quantization scheme to entirely remove the data dependency in the prediction step of SZ such that this step can be performed very efficiently on GPUs. (2) We develop an efficient customized Huffman coding for the SZ compressor on GPUs. (3) We implement cuSZ using CUDA and optimize its performance by improving the utilization of GPU memory bandwidth. (4) We evaluate our cuSZ on five real-world HPC application datasets from the Scientific Data Reduction Benchmarks and compare it with other state-of-the-art methods on both CPUs and GPUs. Experiments show that our cuSZ improves SZ's compression throughput by up to 370.1x and 13.1x, respectively, over the production version running on single and multiple CPU cores, respectively, while getting the same quality of reconstructed data. It also improves the compression ratio by up to 3.48x on the tested data compared with another state-of-the-art GPU supported lossy compressor.more » « less
An official website of the United States government

