@techreport{oai:ipsj.ixsq.nii.ac.jp:00092462,
 author = {幸谷, 智紀 and Tomonori, Kouya},
 issue = {18},
 month = {May},
 note = {実用上重要な 「固い」 常微分方程式を効率的に解くためには陰的解法が相応しい．我々は高次多倍長陰的 Runge-Kutta 法を混合精度反復改良法を用いて高速化し，ブロック三重対角化を行って効率化を図った多倍長精度の ODE ソルバーを開発した．今回はこのアルゴリズム全体に OpenMP による並列化を行い，マルチコア CPU 上において更なる高速化に成功した．本論文では多倍長 ODE ソルバーのアルゴリズムと数値的特性を示し，プロファイリングによってどの程度の性能向上が行われたかを明らかにする．, Implicit algorithms such as implicit Runge-Kutta methods are appropriate to solve “stiff” ordinary differential equations (ODEs) numerically which play important role in various scientific simulations. We have already developed the ODE solver based on high-order multiple precision fully implicit Runge-Kutta (IRK) methods accelerated by using mixed precision iterative refinement method and reduction to block tridiagonal form. Our whole parallelization of IRK methods by using OpenMP can also accelerate the ODE solver successfully. In this paper, we show the numerical property of our ODE solver based on IRK methods and reveal how fast the parallelized IRK process can run through profiling.},
 title = {並列化した多倍長陰的Runge-Kutta法の性能分析},
 year = {2013}
}