New implementations of the Calderon preconditioning for boundary element methods

2019 Fiscal Year Final Research Report

• Project/Area Number: 18K18063
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60100:Computational science-related
• Research Institution: Kyoto University
• Principal Investigator: Niino Kazuki 京都大学, 情報学研究科, 助教 (10728182)
• Project Period (FY): 2018-04-01 – 2020-03-31
• Keywords: Calderonの前処理 / 境界要素法 / 境界積分方程式

Outline of Final Research Achievements

In this research, we developed a new implementation of Calderon's preconditioning, which is one of acceleration methods for iterative linear solvers in boundary element methods. Calderon's preconditioning is known to significantly reduce the iteration numbers of iteration methods. Application of Calderon's preconditioning however takes more computational time for each iteration since use of a certain special basis function, which causes the increase of the computational time, is necessary. We propose an implementation of Calderon's preconditioning, which avoids the use of the special basis function by applying well-known regularizing method to operators appeared in Calderon's preconditioning.

Free Research Field

計算電磁気学

Academic Significance and Societal Importance of the Research Achievements

本研究で開発した数値解法はLaplace方程式やHelmholtz方程式，Maxwell方程式など応用上重要な様々な方程式に適用可能であり，特に自由度が大きい問題に対して効果的であるため，様々な工学の分野で現れる大規模問題を解くための基礎的研究として重要であると考えられる．また本研究では新しい前処理法を開発しただけではなく，この前処理法が一見異なる既存の定式化とよく似ていることを発見し，これによって精度を改善した新しい積分方程式の定式化の開発などへとつながっているため，学術的にも今後の発展性のある研究であると言える．