Development of a hierarchical parallel numerical algorithm for saddle point problems

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K11840
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60090:High performance computing-related
• Research Institution: University of Tsukuba
• Principal Investigator: Tadano Hiroto 筑波大学, 計算科学研究センター, 助教 (50507845)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 鞍点型連立一次方程式 / 階層並列型数値解法 / ブロッククリロフ部分空間反復法

Outline of Final Research Achievements

Saddle point problems appear in many application areas, and a fast solver for these problems is needed. In this research project, we constructed a hierarchical parallel solver for these problems and developed a parallel computing code. We evaluated the parallel performance of this code on the Cygnus Supercomputer, operated at the Center for Computational Sciences, University of Tsukuba, and demonstrated that this solver is suitable for parallel computing environments. In addition, we also developed a highly accurate numerical solver for linear systems with multiple right-hand sides, which is needed in the hierarchical parallel solver.

Free Research Field

数値線形代数

Academic Significance and Societal Importance of the Research Achievements

本研究課題を通して，鞍点型連立一次方程式の階層並列型数値解法を開発することにより，同方程式の反復法による求解難度を下げることができたとともに，並列計算環境に適した手法を構築することができた．また，複数右辺ベクトルをもつ連立一次方程式の高精度数値解法を開発することにより，本研究課題の内容にとどまらず他の分野に対しても貢献できる．