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HIgh-precision numerical analysis of fluid phenomena by the method of fundamental solutions

Research Project

Project/Area Number 18K13455
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionOkayama University of Science (2020-2022)
Kyoto University (2018-2019)

Principal Investigator

Sakakibara Koya  岡山理科大学, 理学部, 講師 (30807772)

Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords基本解近似解法 / Hele-Shaw問題 / 極小曲面 / Plateau問題 / 磁性流体 / 点渦力学系 / Hele-Shaw 問題 / 勾配流 / 構造保存型数値解法 / 接線速度 / 流体力学 / 一様配置法 / 曲率依存型配置法
Outline of Final Research Achievements

The goal of this research was to apply the method of fundamental solutions, known as mesh-free numerical method for partial differential equations, to fluid phenomena. As a result, for the first time in the world, we proposed a spatial discretization for the Hele-Shaw problem that preserves its geometric variational structure in an asymptotic sense, and confirmed its usefulness through mathematical analysis and extensive numerical experiments. We also designed a fast and accurate algorithm for determining the number of minimal surfaces (in particular, the Plateau problem), proved its convergence to minimal surfaces, and demonstrated its usefulness in various concrete examples.

Translated with www.DeepL.com/Translator (free version)

Academic Significance and Societal Importance of the Research Achievements

基本解近似解法は,そのスキームの簡便さ故に主に工学分野で多く応用されてきたが,流体現象を記述する問題に対する応用にはあまり成功していなかった.本研究では,Hele-Shaw問題に対する応用により移動境界問題に対する基本解近似解法の有用性を実証することに成功した.また,高精度であることを活かした極小曲面の数値計算アルゴリズムを提唱しその解析に成功したことで,極小曲面の滑らかな近似を,理論保証込みで初めて可能とした.

Report

(6 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (61 results)

All 2023 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (1 results) Journal Article (8 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 8 results,  Open Access: 4 results) Presentation (50 results) (of which Int'l Joint Research: 10 results,  Invited: 27 results) Remarks (2 results)

  • [Int'l Joint Research] The University of Pennsylvania(米国)

    • Related Report
      2021 Research-status Report
  • [Journal Article] A simple numerical method for Hele-Shaw type problems by the method of fundamental solutions2022

    • Author(s)
      Sakakibara Koya、Shimoji Yusaku、Yazaki Shigetoshi
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 39 Issue: 3 Pages: 869-887

    • DOI

      10.1007/s13160-022-00530-1

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Asymptotic Behavior of Fronts and Pulses of the Bidomain Model2022

    • Author(s)
      Matano Hiroshi、Mori Yoichiro、Nara Mitsunori、Sakakibara Koya
    • Journal Title

      SIAM Journal on Applied Dynamical Systems

      Volume: 21 Issue: 1 Pages: 616-649

    • DOI

      10.1137/21m1416904

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A fully discrete curve-shortening polygonal evolution law for moving boundary problems2021

    • Author(s)
      Sakakibara Koya、Miyatake Yuto
    • Journal Title

      Journal of Computational Physics

      Volume: 424 Pages: 109857-109857

    • DOI

      10.1016/j.jcp.2020.109857

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A new numerical scheme for discrete constrained total variation flows and its convergence2020

    • Author(s)
      Y. Giga, K. Sakakibara, K. Taguchi and M. Uesaka
    • Journal Title

      Numer. Math.

      Volume: 146 Issue: 1 Pages: 181-217

    • DOI

      10.1007/s00211-020-01134-y

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Numerical analysis of constrained total variation flows2020

    • Author(s)
      Sakakibara Koya
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 85

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Bidirectional numerical conformal mapping based on the dipole simulation method2020

    • Author(s)
      Sakakibara Koya
    • Journal Title

      Engineering Analysis with Boundary Elements

      Volume: 114 Pages: 45-57

    • DOI

      10.1016/j.enganabound.2020.01.009

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Structure‐preserving numerical scheme for the one‐phase Hele‐Shaw problems by the method of fundamental solutions2019

    • Author(s)
      Sakakibara, Koya and Yazaki, Shigetoshi
    • Journal Title

      Computational and Mathematical Methods

      Volume: 1 Issue: 6

    • DOI

      10.1002/cmm4.1063

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Numerical approach to three-dimensional model of cellular electrophysiology by the method of fundamental solutions2019

    • Author(s)
      Nakamura, Ken-Ichi; Sakakibara, Koya; Yazaki Shigetoshi
    • Journal Title

      JSIAM Letters

      Volume: 11 Issue: 0 Pages: 17-20

    • DOI

      10.14495/jsiaml.11.17

    • NAID

      130007607539

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] 基本解近似解法による極小曲面の数値解析2023

    • Author(s)
      榊原 航也
    • Organizer
      北陸応用数理研究会2023
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Analysis of the well-conditioned method of fundamental solutions for the Laplace equation2022

    • Author(s)
      Koya Sakakibara
    • Organizer
      Workshop on scientific computing 2022
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 悪条件性を緩和した基本解近似解法の数学解析2022

    • Author(s)
      榊原 航也
    • Organizer
      京都大学NLPDEセミナー
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] 悪条件性を緩和した代用電荷法の数学解析2022

    • Author(s)
      榊原 航也
    • Organizer
      日本応用数理学会2022年度年会
    • Related Report
      2022 Annual Research Report
  • [Presentation] 基本解近似解法の数理2022

    • Author(s)
      榊原 航也
    • Organizer
      第3回若手研究交流会
    • Related Report
      2022 Annual Research Report
  • [Presentation] 基本解近似解法による極小曲面の数値計算2022

    • Author(s)
      榊原 航也
    • Organizer
      愛媛大学解析セミナー
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] 悪条件性を緩和した基本解近似解法の数学解析2022

    • Author(s)
      榊原 航也
    • Organizer
      2022年度応用数学合同研究集会
    • Related Report
      2022 Annual Research Report
  • [Presentation] 代用電荷法によるPlateau問題の数値解析2022

    • Author(s)
      榊原 航也
    • Organizer
      日本応用数理学会環瀬戸内応用数理研究部会第26回シンポジウム
    • Related Report
      2022 Annual Research Report
  • [Presentation] バイドメインモデルのフロント解・パルス解の漸近挙動の数値的考察2022

    • Author(s)
      榊原 航也
    • Organizer
      第35回さいたま数理解析セミナー
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] バイドメインモデルのフロント解とパルス解の漸近挙動2022

    • Author(s)
      榊原 航也
    • Organizer
      第124回北大MMCセミナー
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] バイドメインモデルにおける解の漸近挙動の数値解析2022

    • Author(s)
      榊原 航也,奈良 光紀,俣野 博,森 洋一朗
    • Organizer
      日本応用数理学会第18回研究部会連合発表会
    • Related Report
      2021 Research-status Report
  • [Presentation] 悪条件性を緩和した基本解近似解法の円板領域での数学解析2022

    • Author(s)
      榊原 航也
    • Organizer
      北陸応用数理研究会2022
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] 変形する自己駆動系に対する界面モデルの数値計算2022

    • Author(s)
      榊原 航也,長山 雅晴,物部 治徳
    • Organizer
      日本数学会2022年度年会
    • Related Report
      2021 Research-status Report
  • [Presentation] バイドメインモデルにおけるフロント解・パルス解の漸近挙動2021

    • Author(s)
      榊原 航也
    • Organizer
      第92回京都駅前セミナー
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] 幾何学流の数学・数値解析:構造保存型数値解法とSobolev勾配流2021

    • Author(s)
      榊原 航也
    • Organizer
      日本応用数理学会「若手の会」第2回若手研究交流会
    • Related Report
      2021 Research-status Report
  • [Presentation] バイドメインモデルにおける解の漸近挙動2021

    • Author(s)
      榊原 航也,奈良 光紀,俣野 博,森 洋一朗
    • Organizer
      日本数学会2021年度秋季総合分科会
    • Related Report
      2021 Research-status Report
  • [Presentation] 基本解近似解法を用いた磁性流体のHele-Shaw問題に対する数値計算2021

    • Author(s)
      榊原 航也,下地 優作,矢崎 成俊
    • Organizer
      日本数学会2021年度秋季総合分科会
    • Related Report
      2021 Research-status Report
  • [Presentation] Numerical study on front and pulse solutions in the bidomain model2021

    • Author(s)
      Koya Sakakibara
    • Organizer
      RIMS International conference "Modeling and Mathematical Analysis of Dynamics of Patterns"
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 基本解近似解法を用いた磁性流体のHele-Shaw問題に対する数値計算2021

    • Author(s)
      榊原 航也,下地 優作,矢崎 成俊
    • Organizer
      2021年度応用数学合同研究集会
    • Related Report
      2021 Research-status Report
  • [Presentation] バイドメインモデルにおけるフロント解・パルス解の漸近挙動の数値解析2021

    • Author(s)
      榊原 航也,奈良 光紀,俣野 博,森 洋一朗
    • Organizer
      日本応用数理学会環瀬戸内応用数理研究部会第25回シンポジウム
    • Related Report
      2021 Research-status Report
  • [Presentation] Numerical analysis of constrained total variation flows and its application to the Kobayashi-Warren-Carter model2021

    • Author(s)
      榊原 航也
    • Organizer
      RIMS共同研究(公開型)「偏微分方程式における逆問題とその応用のさらなる展開」
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Asymptotic behavior of fronts and pulses of the bidomain equations2021

    • Author(s)
      榊原 航也
    • Organizer
      令和2年度第1回岡山解析セミナー
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] 材料科学および電気生理学に現れる界面現象の数値解析2021

    • Author(s)
      榊原 航也
    • Organizer
      数学と諸分野の連携に向けた若手数学者交流会2021
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] 界面現象の構造保存型数値解析2020

    • Author(s)
      榊原 航也
    • Organizer
      数値解析セミナー
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] 移動境界問題に対するエネルギー散逸型数値解法2020

    • Author(s)
      榊原 航也、宮武 勇登
    • Organizer
      日本応用数理学会環瀬戸内応用数理研究部会第24回シンポジウム
    • Related Report
      2020 Research-status Report
  • [Presentation] Numerical analysis of interface problem2020

    • Author(s)
      榊原 航也
    • Organizer
      立命館大学数理ファイナンスセミナー
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Structure-preserving numerical scheme for polygonal moving boundary problems2020

    • Author(s)
      Sakakibara, Koya
    • Organizer
      ANZIAM 2020
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] バイドメイン Allen-Cahn/FitzHugh-Nagumo 方程式の数値計算2020

    • Author(s)
      榊原 航也
    • Organizer
      第25回張研コロキウム
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Numerical analysis of constrained total variation flow2019

    • Author(s)
      榊原 航也
    • Organizer
      第73回金沢解析セミナー
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 多様体値全変動流の数値解析~Kobayashi-Warren-Carter モデルの解析に向けて~2019

    • Author(s)
      榊原 航也
    • Organizer
      不連続 Galerkin 有限要素法の数学理論とその周辺:これからの展開
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Bidirectional numerical conformal mapping based on the dipole simulation method2019

    • Author(s)
      Sakakibara, Koya
    • Organizer
      A3 Workshop on fluid dynamics and related topics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 第11回福島応用数学研究集会2019

    • Author(s)
      榊原 航也
    • Organizer
      Hele-Shaw 問題に対する構造保存型数値計算
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 束縛付き全変動流の数値計算スキームについて2019

    • Author(s)
      上坂 正晃,儀我 美一,榊原 航也,田口 和稔
    • Organizer
      日本数学会2019年度年会
    • Related Report
      2019 Research-status Report
  • [Presentation] 閉曲面上の調和測度の数値計算2019

    • Author(s)
      Green, Christopher,榊原 航也,坂上 貴之
    • Organizer
      日本数学会2019年度年会
    • Related Report
      2019 Research-status Report
  • [Presentation] Mathematical analysis of the method of fundamental solutions applied to Helmholtz-type equations2019

    • Author(s)
      Sakakibara, Koya
    • Organizer
      EASIAM 2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Numerical analysis of the method of fundamental solutions applied to Helmholtz-type equations2019

    • Author(s)
      Sakakibara, Koya
    • Organizer
      ICIAM 2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] 流体方程式に対する "安定な" 数値解法2019

    • Author(s)
      榊原 航也
    • Organizer
      RIMS 共同研究(公開型)「宇宙惑星ジェットの数理」
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Numerical analysis of the method of fundamental solutions applied to Helmholtz-type equations2019

    • Author(s)
      Sakakibara, Koya
    • Organizer
      Mini-symposium on Verified Computing and Computer-Assisted Proof
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] メッシュフリー数値解法に基づく移動境界問題の数理解析2019

    • Author(s)
      榊原 航也
    • Organizer
      日本応用数理学会若手の会横断型研究交流会
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 移動境界問題に対するエネルギー散逸型全離散数値計算スキーム2019

    • Author(s)
      榊原 航也
    • Organizer
      数学と現象 in 山中湖
    • Related Report
      2019 Research-status Report
  • [Presentation] Helmholtz 型方程式に対する基本解近似解法の数学解析2019

    • Author(s)
      榊原 航也
    • Organizer
      日本数学会2019年度秋季総合分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] Numerical analysis of constrained total variation flows2019

    • Author(s)
      Giga, Yoshikazu; Sakakibara, Koya; Taguchi, Kazutoshi and Uesaka, Masaaki
    • Organizer
      常微分方程式の数値解法とその周辺 2019
    • Related Report
      2019 Research-status Report
  • [Presentation] Numerical analysis of constrained total variation flows2019

    • Author(s)
      Sakakibara, Koya
    • Organizer
      Mathematical Aspects of Surface and Interface Dynamics 18
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Numerical analysis of discrete total variation flow with manifold constraint2019

    • Author(s)
      Sakakibara, Koya
    • Organizer
      Geometric Analysis and General Relativity
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 移動境界問題に対する全離散エネルギー散逸型数値解法2019

    • Author(s)
      榊原 航也,宮武 勇登
    • Organizer
      2019年度応用数学合同研究集会
    • Related Report
      2019 Research-status Report
  • [Presentation] Numerical scheme for solving Hele-Shaw problems based on the method of fundamental solutions2019

    • Author(s)
      Sakakibara, Koya; Yazaki, Shigetoshi
    • Organizer
      ANZIAM2019
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] 基本解近似解法による点渦力学系の数値解析2018

    • Author(s)
      榊原 航也
    • Organizer
      京都大学応用数学セミナー
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Unified numerical scheme for several types of Hele-Shaw problems by the method of fundamental solutions2018

    • Author(s)
      Sakakibara, Koya; Yazaki, Shigetoshi
    • Organizer
      The 5th Joint Workshop of A3 Foresight Program "Mathematics of Biology, Fluid Dynamics and Material Sciences"
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 様々な Hele-Shaw 型問題に対する基本解近似解法による構造保存型数値解法2018

    • Author(s)
      榊原 航也
    • Organizer
      数学と現象:Mathematics and Phenomena in Miyazaki
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 極小曲面上の点渦力学系:数値解析2018

    • Author(s)
      榊原 航也
    • Organizer
      環瀬戸内ワークショップ
    • Related Report
      2018 Research-status Report
    • Invited
  • [Remarks] 榊原航也の個人Webページ

    • URL

      https://sites.google.com/site/koyasakakibara/home/

    • Related Report
      2021 Research-status Report
  • [Remarks] Koya Sakakibara's Homepage

    • URL

      https://sites.google.com/site/koyasakakibara/

    • Related Report
      2020 Research-status Report 2019 Research-status Report

URL: 

Published: 2018-04-23   Modified: 2024-01-30  

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