Development of new efficient structure-preserving numerical methods based on model reductions

2021 Fiscal Year Final Research Report

• Project/Area Number: 17H02826
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Computational science
• Research Institution: The University of Tokyo
• Principal Investigator: Matsuo Takayasu 東京大学, 大学院情報理工学系研究科, 教授 (90293670)
• Co-Investigator(Kenkyū-buntansha): 相島 健助 法政大学, 情報科学部, 准教授 (40609658)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: 数値解析 / 構造保存解法 / モデル縮減

Outline of Final Research Achievements

In this research plan, we aimed at the development of a new structure-preserving numerical methods incorporating with model reduction techniques. As results, we have verified the effectiveness of some symplectic model reduction techniques, and obtained a new structure-preserving method for dissipative systems with model reduction mechanism, as desired. In addition to that, in search of such new methods, we have obtained several new fundamental tools including a new structure-preserving method based on Poisson and Nambu brackets, and a rigorous theoretical analysis for dynamical mode decompositions.

Free Research Field

数値解析

Academic Significance and Societal Importance of the Research Achievements

数値解析，とりわけ微分方程式に対する構造保存解法は，現代の科学・工学を支える重要な技術である．本研究は，拡大を続ける現代科学・工学の諸問題に対処するために，この技術をモデル縮減の技法を採り入れて進化させるものである．これにより，従来，既存の構造保存解法では解けなかった大規模問題が解かれることが期待される．また，構造保存解法や動的モード分解などに関する基礎的知見も得られ，数値解析学の前進に寄与した．