Development of a numerical method according a framework of weak-form discretisation scheme and its experimental evaluation

• Project/Area Number: 15K04752
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Computational science
• Research Institution: University of Yamanashi
• Principal Investigator: KATO Hatsuhiro 山梨大学, 大学院総合研究部, 准教授 (00270174)
• Co-Investigator(Kenkyū-buntansha): 加藤 初儀 苫小牧工業高等専門学校, 創造工学科, 教授 (80224525) ; 石井 孝明 山梨大学, 大学院総合研究部, 教授 (40262323)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2016: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000); Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
• Keywords: 重調和解析 / 弱形式理論 / 輻射境界条件 / 局在波 / 数値解析 / 屈曲波 / 逐次伝達法 / 近接場 / 近接場ラップ / 弱形式スキーム / 弾性導波路 / フィルタ / ファノ効果

Outline of Final Research Achievements

We have extended the recursive transfer method (RTM) that is a novel numerical method being developed under The framework of weak discretisation. The efficiency of RTM　is also confirmed experimentally through the localised wave that appears in an elastic system. The main achievements are as follows: 1) Improvement of numerical accuracy using freedom of shape function. 2) Extension of RTM using scalene quadrilateral elements included in the discretisation mesh. 3) Development of an experiment method to extract scattering waves from the incident wave in elastic wave guide. 4) Detection and application of resonance reflection that is involved with the localised wave. For next stage, we are planning to apply RTM to the quantum scattering after improving the radiation boundary condition.

Research Products

• [Journal Article] Mechanics shape function of quadrilateral element composed of subdivision triangles for recursive transfer method (2017)
  • Author(s): Kato Hatsuhiro、Kato Hatsuyoshi、Naito Yoshimasa
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 35 Issue: 1 Pages: 277-295
  • DOI: 10.1007/s13160-017-0281-9
  • NAID: 210000186528
  • Peer Reviewed / Open Access
• [Journal Article] The control of resonance curve using the shape modulation of the scattering (2017)
  • Author(s): Hatsuhiro Kato, Yoshimasa Naito, and Takaaki Ishii, and Hatsuyoshi Kato
  • Journal Title: Proceeding on Meeting of the Acoustical Society of America Volume: 29 Pages: 1-10
  • DOI: 10.1121/2.0000387
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] 弾性導波路における共鳴反射の検出 (2016)
  • Author(s): 加藤初弘，石井 孝明，加藤初儀,
  • Journal Title: 電子情報通信学会論文誌A Volume: J98-A Pages: 580-586
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Accuracy of weak-form discretisation and extension of recursive transfer method for scattering problems governed by fourth-order differential equation (2016)
  • Author(s): Hatsuhiro Kato and Hatsuyoshi Kato
  • Journal Title: Journal of the Physical Society of Japan Volume: 85 Issue: 5 Pages: 054001-054001
  • DOI: 10.7566/jpsj.85.054001
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] 弾性導波路におけるＳパラメータの抽出方法の開発 (2015)
  • Author(s): 内藤吉優，加藤 初弘，石井孝明，加藤 初弘
  • Journal Title: 電子情報通信学会技術研究報告 Volume: US2015-48 Pages: 13-16
  • Acknowledgement Compliant
• [Presentation] 弾性導波路におけるFano共鳴 (2017)
  • Author(s): 加藤初弘，加藤初儀，松井直道
  • Organizer: 電子情報通信学会 2018年総合大会
• [Presentation] The control of resonance curve using the shape modulation of the scattering (2016)
  • Author(s): Yoshimasa Naito, Hatsuhiro Kato and Takaaki Ishii
  • Organizer: 5th Joint Meeting Acoustical Society of America and Acoustical Society of Japan
  • Place of Presentation: Honolulu, Hawaii, USA
  • Year and Date: 2016-11-28
  • Int'l Joint Research
• [Presentation] 細分化四角形要素を用いたRTMによる散乱問題の数値計算法 (2016)
  • Author(s): 加藤初弘，加藤初儀
  • Organizer: 日本応用数理学会 「常微分方程式の数値解析とその周辺 2016」
  • Place of Presentation: 大阪市 阪大豊中キャンパス
  • Year and Date: 2016-07-04
• [Presentation] 弾性導波路におけるＳパラメータの抽出方法の開発 (2015)
  • Author(s): 内藤吉優， 加藤 初弘，石井孝明，加藤 初儀
  • Organizer: 電子情報通信学会 超音波研究会
  • Place of Presentation: 第1滝本（北海道・登別市）
  • Year and Date: 2015-09-03
• [Presentation] 弱形式離散化スキーム逐次伝達法を用いた散乱問題の数値計算法の提案 (2015)
  • Author(s): 加藤初弘，加藤初儀
  • Organizer: 日本応用数理学会 「第４４回数値計算シンポジウム」
  • Place of Presentation: ぶどうの丘（山梨県・甲州市）
  • Year and Date: 2015-06-08
• [Remarks]
  • URL: http://www.szr.yamanashi.ac.jp/lab/kato/Okura/KAKENHI2015/index.htm
• [Remarks] Extention ofBiharmonic Analysis
  • URL: http://www.szr.yamanashi.ac.jp/lab/kato/Okura/index.htm
• [Remarks] Reserch Subject and Published Articles
  • URL: http://www.szr.yamanashi.ac.jp/lab/kato/Okura/index.htm