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  • A New Compression Scheme of Sparse Matrix Formats for Accurate Numerical Simulation on Site Environment with GPGPU

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近年,計算機の高性能化にともない数値シミュレーションをオンサイトでリアルタイムに実行し,様々な産業に応用することが期待されている.このようなシミュレーションは,GPGPUを利用することによって実用的な計算時間での実行が期待できるが,メモリ容量の制約が大きな問題点である.そこで本稿では数値シミュレーションの代表的手法であるFinite Element Method(FEM)で現れる疎行列のメモリ使用量削減手法を提案する.提案手法では,疎行列の列番号を表す値をパッキングし,メモリに格納する値の数を削減する.複数の疎行列による評価では,15個中13個において従来手法に対しメモリ使用量を削減し,最大で26.3%の削減率となった.また,オンサイト実施が期待される分野の一例として心臓シミュレーション用の疎行列にも適用したところ,メモリ使用量が20.6%削減された.

Recent years, performing high-precision numerical simulations on-site and adapting the results to various industries are expected, as the computing power has been increasing. Although such simulations can possibly be executed in a practical time with GPUs, some of them do not fit in GPUs due to their limited memory capacity. To solve this problem, we proposed a new compression scheme of sparse matrix storage formats. Assuming that some parts of the column indices in the sparse matrix are a consecutive and such those parts can be described with its minimum and maximum column number. In our experiments, we reduced the memory usage of general sparse matrices up to 26.3% in 13 out of 15 matrices compared with conventional storage. Also, we reduced the memory usage of matrices used in a heart simulation up to 20.6%.


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