An assessment of the efficiency of isogeometric boundary integral methods

Research Project

Project/Area Number	18K19783
Research Category	Grant-in-Aid for Challenging Research (Exploratory)
Allocation Type	Multi-year Fund
Review Section	Medium-sized Section 60:Information science, computer engineering, and related fields
Research Institution	Kyoto University
Principal Investigator	Nishimura Naoshi 京都大学, 情報学研究科, 教授 (90127118)
Co-Investigator(Kenkyū-buntansha)	新納和樹京都大学, 情報学研究科, 助教 (10728182) 吉川仁京都大学, 情報学研究科, 准教授 (90359836)
Project Period (FY)	2018-06-29 – 2020-03-31
Project Status	Completed (Fiscal Year 2019)
Budget Amount *help	¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000) Fiscal Year 2019: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000) Fiscal Year 2018: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Keywords	isogeometric 解析 / 境界積分法 / Maxwell方程式 / isogeometric解析 / Nystroem法
Outline of Final Research Achievements	The isogeometric analysis, investigated actively in computational mechanics recently, utilises NURBS functions for both geometrical modelling and interpolation of the unknown functions. However, the significance of this approach in boundary integral methods needs to be carefully reexamined. This study discusses essential features of the isogeometric analysis which allow the development of boundary integral methods which can achieve the balance between the computational cost and the accuracy. Specifically, we combine the high quality geometric modelling used in isogeometric analysis with the Nystroem method to obtain a highly accurate solver of boundary integral equations. We also propose a collocation boundary integral method for Maxwell's equations based on the isogeometric analysis.
Academic Significance and Societal Importance of the Research Achievements	本研究は，従来CADとの連携等の本質的でない側面が強調されてきたisogeometric解析において，境界積分法の精度向上の立場から新しい視点を提供した．実際，幾何学形状と未知関数の基底関数の共通化に拘るより，要素のもたらす不要な特異性を除去することが重要であることを示した．この考え方に立って，isogeometric解析とNystroem法との併用という高精度の解法を得ることができた．また同様な考え方から従来困難であったMaxwell方程式の積分方程式の選点法による解法を得ることができ，電磁波解析の計算効率の向上に貢献した．