Authors: Tsuyoshi Ichimura and Kohei Fujita (University of Tokyo, RIKEN); Ryota Kusakabe (University of Tokyo); Kentaro Koyama (Fujitsu Ltd); Sota Murakami and Yuma Kikuchi (University of Tokyo); Takane Hori and Muneo Hori (Japan Agency for Marine-Earth Science and Technology); Hikaru Inoue, Takafumi Nose, and Takahiro Kawashima (Fujitsu Ltd); and Lalith Maddegedara (University of Tokyo)
Abstract: We develop a stochastic finite element method with ultra-large degrees of freedom that discretize probabilistic and physical spaces using unstructured second-order tetrahedral elements with double precision using a mixed-precision implicit iterative solver that scales to the full Fugaku system and enables fast Uncertainty Quantification (UQ). The developed solver designed to attain high performance on a variety of CPU/GPU-based supercomputers enabled solving 37 trillion degrees-of-freedom problem with 19.8% peak FP64 performance on full Fugaku (89.8 PFLOPS) with 87.7% weak scaling efficiency, corresponding to 224-fold speedup over the state of the art solver running on full Summit. This method, which has shown its effectiveness via solving huge (32-trillion degrees-of-freedom) practical problems, is expected to be a breakthrough in damage mitigation, and is expected to facilitate the scientific understanding of earthquake phenomena and have a ripple effect on other fields that similarly require UQ.
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