A Fast Scalable Implicit Solver with Concentrated Computation for Nonlinear Time-Evolution Problems on Low-Order Unstructured Finite Elements

• Published in: 2018 IEEE International Parallel and Distributed Processing Symposium (IPDPS) pp. 620 - 629
• Main Authors: Ichimura, Tsuyoshi, Fujita, Kohei, Horikoshi, Masashi, Meadows, Larry, Nakajima, Kengo, Yamaguchi, Takuma, Koyama, Kentaro, Inoue, Hikaru, Naruse, Akira, Katsushima, Keisuke, Hori, Muneo, Maddegedara, Lalith
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-05-2018
• Subjects: Computational modeling; Computer architecture; Concentrated Computation; Earthquakes; Fast Scalable Implicit Solver for Nonlinear Time evolution Problems; Kernel; Low-order Unstructured Finite Elements; Mathematical model; Sparse matrices; Supercomputers; Time-parallel
• ISSN: 1530-2075
• DOI: 10.1109/IPDPS.2018.00071

Many supercomputers are shifting to architectures with low B (byte/s; memory transfer capability) per F (FLOPS capability) ratios. However, utilizing increased F is difficult for applications that inherently require large B. Targeting an implicit unstructured low-order finite-element analysis solver, which typically requires large B, we have developed a concentrated computation algorithm that yields significant performance improvements on low B/F supercomputers. 35.7% peak performance was achieved for a sparse matrix-vector multiplication kernel, and 15.6% peak performance was achieved for the whole solver on the second generation Xeon Phi-based Oakforest-PACS. This is 5.02 times faster than (and 6.90 times the peak performance of) the state-of-the-art solver (the SC14 Gordon Bell finalist solver). On Oakforest-PACS, the proposed solver was approximately 2.42 times faster than the state-of-the-art solver running on the K computer. The proposed approach has implications for systems and applications and is expected to have significant impact on various fields that use finite-element methods for nonlinear time evolution problems.