• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Visualizaion of exteremal quasiconformal mappings

Research Project

Project/Area Number 16K16061
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field High performance computing
Research InstitutionYamanashi Eiwa College

Principal Investigator

Shimauchi Hirokazu  山梨英和大学, 人間文化学部, 助教 (90759200)

Project Period (FY) 2016-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords極値的擬等角写像 / 数値擬等角写像 / 擬等角写像 / 可視化 / 高性能計算 / Loewner方程式
Outline of Final Research Achievements

In this project, the visualization method of extremal quasiconformal mappings was studied. We constructed an approximant as a piecewise linear mapping, which is obtained by the least squares solution of an overdetermined linear system. The Beltrami coefficients and boundary correspondence was used for our linear system. Numerical experiments show high accuracy of approximants.
Furthermore, we studied the numerical construction of the Loewner flow in view of application for quasiconformal mappings. The approximant was constructed as a family of polynomials. We proved the convergence of the coefficients of polynomial. The results were published in a mathematical journal and presented on international conferences.

Report

(3 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • Research Products

    (6 results)

All 2018 2017

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (5 results) (of which Int'l Joint Research: 3 results)

  • [Journal Article] On a numerical algorithm for the solution of the radial Loewner equation2018

    • Author(s)
      Ikkei Hotta, Hirokazu Shimauchi
    • Journal Title

      Math. Methods Appl. Sci.

      Volume: 41 Issue: 2 Pages: 714-723

    • DOI

      10.1002/mma.4640

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Presentation] Visualizing the solution of the radial Loewner equation2017

    • Author(s)
      Hirokazu Shimauchi
    • Organizer
      The International Conference on Computational Methods and Function Theory 2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A numerical algorithm for solving the Loewner equation2017

    • Author(s)
      Hirokazu Shimauchi
    • Organizer
      The 25th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical solution of the radial Loewner equation2017

    • Author(s)
      Hirokazu Shimauchi
    • Organizer
      The XXVth International Conference on Integrable Systems and Quantum symmetries, Czech Technical University
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical computation of the radial Loewner flow2017

    • Author(s)
      島内 宏和
    • Organizer
      等角写像・値分布論合同研究集会
    • Place of Presentation
      千葉大学(千葉県千葉市稲毛区)
    • Related Report
      2016 Research-status Report
  • [Presentation] Numerical solution of the radial Loewner equation2017

    • Author(s)
      島内 宏和
    • Organizer
      日本数学会・2017年度年会
    • Place of Presentation
      首都大学東京(東京都八王子市)
    • Related Report
      2016 Research-status Report

URL: 

Published: 2016-04-21   Modified: 2019-03-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi