Study of structure preserving method for Einstein equations

2022 Fiscal Year Final Research Report

• Project/Area Number: 20K03740
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Waseda University
• Principal Investigator: Yoneda Gen 早稲田大学, 理工学術院, 教授 (90277848)
• Co-Investigator(Kenkyū-buntansha): 土屋 拓也 八戸工業大学, 基礎教育研究センター, 准教授 (50632139)
• Project Period (FY): 2020-04-01 – 2023-03-31
• Keywords: Einstein方程式 / 高精度数値計算 / 構造保存型数値計算 / 固有値解析

Outline of Final Research Achievements

In this study, we investigated a numerical method that preserves the constraints of the Einstein equations, which are classified as the constrained nonlinear hyperbolic equations. As a result, we have established a evaluation criterion for the accuracy of constraint (constraint's order of accuracy(COA)), and have clarified the differences between COA and the accuracy of evolution equation (evolution's order of accuracy(EOA)). Furthermore, we proposed some formulations of the Einstein equations to make more stable simulations, and performed some high accuracy numerical results of the gravitational collapse simulations.

Free Research Field

相対性理論

Academic Significance and Societal Importance of the Research Achievements

発展方程式を扱う数値計算における精度は、一般には発展方程式の離散化の際の打ち切り誤差から生じる精度を指す。一方、拘束条件付き発展方程式の場合は、拘束条件から生じる精度も存在する。これまではこの区別があまり明確でなかった。今回、拘束条件に対する精度(constraint's order of accuracy(COA))と発展方程式に対する精度(evolution's order of accuracy(EOA))の違いを明確にしたことで、数値計算の精度についてのより正しい理解を促す結果となると考えている。