2000 Fiscal Year Annual Research Report

代用電荷法と数値等角写像に関する総合的研究

Research Project

Project/Area Number	12440029
Research Institution	Ehime University
Principal Investigator	天野要愛媛大学, 工学部, 教授 (80113512)
Co-Investigator(Kenkyū-buntansha)	井上哲男神戸商船大学, 商船学部, 教授 (50031448) 岡野大愛媛大学, 工学部, 助手 (90294785) 緒方秀教愛媛大学, 工学部, 講師 (50242037) 杉原正顯名古屋大学, 大学院・工学研究科, 教授 (80154483) 四ツ谷晶二龍谷大学, 理工学部, 教授 (60128361)
Keywords	代用電荷法 / 数値等角写像 / ボテンシャル問題 / 基本解 / 複素関数論 / 数値解析
Research Abstract	研究の主題は,ポテンシャル問題の高精度高速解法として知られている代用電荷法を適用して,多重連結領域から様々な形状の標準スリット領域への統一的な数値等角写像の方法を開発することである.本年度の研究成果の概要は次の通りである. 1.これまでの研究を集成し,非有界な多重連結領域から平行スリット領域,円弧スリット領域,放射スリット領域への統一的な数値等角写像の方法を再構成した.これらの等角写像は2次元ポテンシャル流解析への応用上重要な広く知られた問題であり,簡単で精度の高い近似写像関数の構成法は理論と応用を繋ぐべきmissing linkであった.この成果は創立40周年記念論文として情報処理学会論文誌42巻に掲載の予定である. 2.有界な多重連結領域から円弧スリット単位円板領域への数値等角写像の方法を提案し,その有効性を数値実験的に検証した.この問題は多重連結領域の等角写像として基本的なものである.単一のJordan閉曲線で囲まれた単連結領域から単位円板領域への場合はRiemannの写像定理として知られている. 主題に関連して,非有界な多重連結領域の数値等角写像を様々なポテンシャル流に適用し,その有効性を数値実験的に検証した.近似写像関数の一様収束性等に関する理論的な知見も得られている.現在,代用電荷法のスキームと連立1次方程式の可解性,周期的領域やPoisson方程式への適用性,等に関する研究が進行中である. なお,上記の数値等角写像の方法には積分方程式法も適用可能である.数値積分法に関しても,2重指数関数型数値積分公式(DE公式)の適用性に関するいくつかの成果が得られている.

Research Products
(18 results)

All Other

All Publications (18 results)

[Publications] 天野要: "代用電荷法による非有界な多重連結領域の統一的な数値等角写像の方法"情報処理学会論文誌. 42・3(掲載予定). (2001)
[Publications] Amano,K.: "Continuous schemes of numerical conformal mapping by the charge simulation method"Information. 4・1(掲載予定). (2001)
[Publications] Amano,K.: "Numerical conformal mapping by the charge simulation method and its application to potential flow analysis"Proceedings of the Second ISAAC (International Society for Analysis,its Applications and Computation) Congress . 1. 329-336 (2000)
[Publications] 天野要: "代用電荷法による円弧スリット単位円板領域への数値等角写像の方法"情報処理学会論文誌. 41・4. 998-1008 (2000)
[Publications] Ogata,H.: "DE-type quadrature formulae for Cauchy principal-value integrals and for Hadamard finite-part integrals"Proceedings of the Second ISAAC (International Society for Analysis,its Applications and Computation) Congress. 1. 357-336 (2000)
[Publications] Okano,D.: "An integral equation method of numerical conformal mapping onto parallel, circular, and radial slit domains"Proceedings of the Second ISAAC (International Society for Analysis,its Applications and Computation) Congress. 1. 375-382 (2000)
[Publications] 片山茂: "数値等角写像による淀み点の数値計算"愛媛大学工学部紀要. 20(掲載予定). (2001)
[Publications] Inoue,T.: "Uniform convergence of numerical conformal mappings of interior domains"International Journal of Mathematics and Mathematical Sciences. 24・7. 461-467 (2000)
[Publications] Inoue,T.: "Theoretical scheme on numerical conformal mapping of unbounded multiply connected domains by fundamental solution method"International Journal of Mathematics and Mathematical Sciences. 24・2. 129-137 (2000)
[Publications] Inoue,T.: "Program to compute Chebyshev points and the numerical experiment"Information. 3・2. 159-166 (2000)
[Publications] Morishita,H.: "Structural change of solutions for a scalar curvature equation"Differential and Integral Equations. 14・3(to appear). (2001)
[Publications] Yanagida,E.: "A unified approach to the structure of radial solutions for semilinear elliptic problems"Japan Journal of Industrial and Applied mathematics. 18・2(to appear). (2001)
[Publications] Sugihara,M.: "Sinc-Calerkin method with the double exponential transformation for the two-point boundary value problems"Proceedings of the 5th China-Japan Seminar on Numerical Mathematics. (to appear).
[Publications] 藤野清次: "CG法に対するModified IC分解の作用に関する一考察"Information. (to appear).
[Publications] Mori,M.: "The double exponential transformation in numerical analysis"Nmerical Analysis in the 20th Century Vol.V : Quadrature and Orthogonal Polynomials, Journal of Computational and Applied Mathematics. 127(to appear).
[Publications] Sugihara,M.: "Justification of a formal derivation of the Eular-Maclaurin summation formula"Proceedings of the Second ISAAC (International Society for Analysis,its Applications and Computation) Congress. (to appear).
[Publications] Zhang,S.-L.: "Necessary and sufficient conditions for the convergence of orthomin(k) on singular and inconsistent linear sysytems"Numerische Mathematik. 87. 391-405 (2000)
[Publications] Ito,H.: "Aharonov-Bohm effect in scattering by point-like magnetic fields at large separation"Annales Henri Poincar'e. (to appear).

2000 Fiscal Year Annual Research Report

代用電荷法と数値等角写像に関する総合的研究

Principal Investigator

天野 要 愛媛大学, 工学部, 教授 (80113512)

Research Products

[Publications] 天野要: "代用電荷法による非有界な多重連結領域の統一的な数値等角写像の方法"情報処理学会論文誌. 42・3(掲載予定). (2001)

[Publications] Amano,K.: "Continuous schemes of numerical conformal mapping by the charge simulation method"Information. 4・1(掲載予定). (2001)

[Publications] Amano,K.: "Numerical conformal mapping by the charge simulation method and its application to potential flow analysis"Proceedings of the Second ISAAC (International Society for Analysis,its Applications and Computation) Congress . 1. 329-336 (2000)

[Publications] 天野要: "代用電荷法による円弧スリット単位円板領域への数値等角写像の方法"情報処理学会論文誌. 41・4. 998-1008 (2000)

[Publications] Ogata,H.: "DE-type quadrature formulae for Cauchy principal-value integrals and for Hadamard finite-part integrals"Proceedings of the Second ISAAC (International Society for Analysis,its Applications and Computation) Congress. 1. 357-336 (2000)

[Publications] Okano,D.: "An integral equation method of numerical conformal mapping onto parallel, circular, and radial slit domains"Proceedings of the Second ISAAC (International Society for Analysis,its Applications and Computation) Congress. 1. 375-382 (2000)

[Publications] 片山茂: "数値等角写像による淀み点の数値計算"愛媛大学工学部紀要. 20(掲載予定). (2001)

[Publications] Inoue,T.: "Uniform convergence of numerical conformal mappings of interior domains"International Journal of Mathematics and Mathematical Sciences. 24・7. 461-467 (2000)

[Publications] Inoue,T.: "Theoretical scheme on numerical conformal mapping of unbounded multiply connected domains by fundamental solution method"International Journal of Mathematics and Mathematical Sciences. 24・2. 129-137 (2000)

[Publications] Inoue,T.: "Program to compute Chebyshev points and the numerical experiment"Information. 3・2. 159-166 (2000)

[Publications] Morishita,H.: "Structural change of solutions for a scalar curvature equation"Differential and Integral Equations. 14・3(to appear). (2001)

[Publications] Yanagida,E.: "A unified approach to the structure of radial solutions for semilinear elliptic problems"Japan Journal of Industrial and Applied mathematics. 18・2(to appear). (2001)

[Publications] Sugihara,M.: "Sinc-Calerkin method with the double exponential transformation for the two-point boundary value problems"Proceedings of the 5th China-Japan Seminar on Numerical Mathematics. (to appear).

[Publications] 藤野清次: "CG法に対するModified IC分解の作用に関する一考察"Information. (to appear).

[Publications] Mori,M.: "The double exponential transformation in numerical analysis"Nmerical Analysis in the 20th Century Vol.V : Quadrature and Orthogonal Polynomials, Journal of Computational and Applied Mathematics. 127(to appear).

[Publications] Sugihara,M.: "Justification of a formal derivation of the Eular-Maclaurin summation formula"Proceedings of the Second ISAAC (International Society for Analysis,its Applications and Computation) Congress. (to appear).

[Publications] Zhang,S.-L.: "Necessary and sufficient conditions for the convergence of orthomin(k) on singular and inconsistent linear sysytems"Numerische Mathematik. 87. 391-405 (2000)

[Publications] Ito,H.: "Aharonov-Bohm effect in scattering by point-like magnetic fields at large separation"Annales Henri Poincar'e. (to appear).

天野要愛媛大学, 工学部, 教授 (80113512)