Optimising Sparse Matrix Vector multiplication for large scale FEM problems on FPGA
Optimising Sparse Matrix Vector multiplication for large scale FEM problems on FPGA
复制标题
优化 FPGA 上大规模 FEM 问题的稀疏矩阵向量乘法
DOI：
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发表时间：
2016
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通讯作者：
S. Sherwin
中科院分区：
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作者：
Paul Grigoras;P. Burovskiy;W. Luk;S. Sherwin
稀疏矩阵向量乘法（SpMV）是许多科学应用中的重要核心。在这项工作中，我们提出了一种架构和一种自动定制方法来检测和优化块对角稀疏矩阵的架构。我们在光谱/hp有限元方法的背景下，使用局部矩阵装配方法来评估所提出的方法。这一问题导致了一个具有块对角矩阵的线性方程组的大型稀疏系统，通常使用预条件共轭梯度等迭代方法来求解。所提出的架构的效率与所提出的定制方法的有效性相结合，将BRAM资源利用率降低了10倍，同时实现了与现有最先进设计相同的吞吐量，并且需要最终用户最少的开发工作。在有限元方法的背景下，我们的方法可以解决比以前更大的问题，使fpga适用于更有趣的高性能计算问题。
Sparse Matrix Vector multiplication (SpMV) is an important kernel in many scientific applications. In this work we propose an architecture and an automated customisation method to detect and optimise the architecture for block diagonal sparse matrices. We evaluate the proposed approach in the context of the spectral/hp Finite Element Method, using the local matrix assembly approach. This problem leads to a large sparse system of linear equations with block diagonal matrix which is typically solved using an iterative method such as the Preconditioned Conjugate Gradient. The efficiency of the proposed architecture combined with the effectiveness of the proposed customisation method reduces BRAM resource utilisation by as much as 10 times, while achieving identical throughput with existing state of the art designs and requiring minimal development effort from the end user. In the context of the Finite Element Method, our approach enables the solution of larger problems than previously possible, enabling the applicability of FPGAs to more interesting HPC problems.