1999 Fiscal Year Annual Research Report

複雑系の数値解析と最適制御の研究

Research Project

Project/Area Number	10440025
Research Institution	Chiba University
Principal Investigator	河原田秀夫千葉大学, 工学部, 教授 (90010793)
Co-Investigator(Kenkyū-buntansha)	加古孝電気通信大学, 電気通信学部, 教授 (30012488) 田端正久九州大学, 大学院・数理学研究科, 教授 (30093272) 森正武京都大学, 数理解析研究所, 教授 (20010936) 今井仁司徳島大学, 工学部, 教授 (80203298) 松葉育雄千葉大学, 工学部, 教授 (30251177)
Keywords	複雑系 / 油濁 / 沿岸生態系 / 大規模連立一次方程式 / 反復解法 / 有限要素法 / Navier-Stokes方程式 / ニューラルネットワーク
Research Abstract	本研究を遂行する上で重要な国際研究集会を研究分担者の協力を得て、行うことができた。それは、「第12回領域分割法に関する国際会議(1999年10月25-29日、千葉大学)」であり、招待外国人と十分な時間をとって、研究討議、交流を行うことができた。研究組織としての研究実績内容として、次の各項があげられる。 (1)「複雑系」の一つの問題として「油濁の沿岸生態系への影響」に関する数理模型の構築とそのシミュレーションを行った。それにより、沿岸生態系に対する油濁負荷を軽減する技術の開発に関する知見を得、関連する研究グループとの研究交流が進んだ。 (2)大規模行列に対する反復解法および精度保証付き数値計算法に進展があった。これは、対称ではあるが固有値に負の値を含む大規模行列を係数にもつ連立1次方程式に対する解法や、楕円型固有値問題の精度保証に関する成果である。 (3)流れの自由境界値問題に関する数値解祈に成果があった。これは、表面張力を考慮した非定常非圧縮性流体の自由境界値問題や、自由境界値問題におけるカオス現象の数値解析手法の開発が行われたことである。 (4)領域分割法の研究に成果があった。それは、外部無限領域へ接続する有界領域における波動伝播について研究である。この手法の応用として、ある音声合成の数値計算を行い、導波路の周波数応答特性に関して興味深い結果が得られた。 (5)ニューラルネットワークに情報理論を持ちこみ,符号化理論の立場から始めて記憶容量を求めることに成功した. 以上の研究成果は、次年度の研究につながり、本研究の課題達成に寄与するものである。

Research Products

(18 results)

All Other

All Publications (18 results)

[Publications] H. Kawarada: "Optimal Shape of Pine for Sound Absorption in Water"Proceeding of 11th International Conference on Domain Decomposition Metheds. 270-281 (1999)
[Publications] H. Kawarada: "Wave Breaking Phenomenon on the Shore and Coastal Ecosystems"GAKUTO International Series, Mathematical Sciences and Applications. Vol.12. 65-74 (1999)
[Publications] T. Ooura: "A robust double exponential formula for Fourier-type integrals"J. Comput. Appl. Math.. 112巻・1/2号. 229-241 (1999)
[Publications] K. Itakura: "An error analysis of streaklines as curves"Japan Journal of Industrial and Applied Mathematics. 16. 1-23 (1999)
[Publications] A. Suzuki: "Numerical solution of an ansteady earth's mantle convection problem by a stabilized finite element method"Theoretical and Applied Mechanics. 48. 371-378 (1999)
[Publications] M. Tabata: "A finite element analysis of a linearized problem of the Navier-Stokes equations with surface tention"SIAM Journal on Numerical Analysis. (to appear).
[Publications] M. T. Nakao: "Numerical verifications of eigenvalues of second-order elliptic operators"Japan Journal of Industrial and Applied Mathematics. 16. 307-320 (1999)
[Publications] K. Nagatou: "An approach to the numerical verification of solutions for nonlinear elliptic problems with local uniqueness"Numerical Functional Analysis and Optimization. 20. 543-565 (1999)
[Publications] Y. Watanabe: "A numerical verification method of solutions for the Navier-Stokes equations"Reliable Computing. 5. 347-357 (1999)
[Publications] T. Kako: "Numerical simulation of wave propagation phenomena in vocal tract and domain decomposition method"Domain decomposition method in science and engineering Proceeding of the 11th International Conference on Domain Decomposition Methods in Greenwich, UK. 267-269 (1999)
[Publications] F. Chiba: "Stability and error analyses by energy estimate for Newmark's method"Reserch Report NIFS-PRO Series. NIFS-PRO-40. 82-91 (1999)
[Publications] H. Suyari: "Information theoritical approach to the storage capacity of neural networks with binary weights"Phys. Rev. E,. 6・4. 4576-4579 (1999)
[Publications] H. Suyari: "Storage capacity of neural networks with binary weights using the minimum distance between input patterns"Proceedings of International Joint Conference on Neural Networks (IJCNN), Washington D.C.. 62-62 (1999)
[Publications] H. Imai: "Motion of Spirals by Crystalline Curvature"Mathematial Modelling and Numerical Analysis. 33・4. 797-806 (1999)
[Publications] H. Imai: "On Numerical Simulation of Partial Differential Equations in Infinite Precision"Advances in Mathematical Sciences and Applications. 9・2. 1007-1016 (1999)
[Publications] H. Imai: "A Crystalline Motion of Spiral-Shaped Curves with Symmety"Journal of Mathematical Analysis and Applications. 240・1. 115-127 (1999)
[Publications] N. Ishimura: "Nonexistence of monotonic solutions of some third order ODE relative to the Kuramoto-Sivashinsky equation"Tiwanese Journal of mathematics. (to appear). (2000)
[Publications] T. Hanada: "Numerical analysis of Eguchi-Oki-Matsumura equations"GAKUTO International Series, Mathematical Sciences and Applications, Advances in numerical mathematics in Japan and China. 12. 213-222 (1999)

1999 Fiscal Year Annual Research Report

複雑系の数値解析と最適制御の研究

Principal Investigator

河原田 秀夫 千葉大学, 工学部, 教授 (90010793)

Research Products

[Publications] H. Kawarada: "Optimal Shape of Pine for Sound Absorption in Water"Proceeding of 11th International Conference on Domain Decomposition Metheds. 270-281 (1999)

[Publications] H. Kawarada: "Wave Breaking Phenomenon on the Shore and Coastal Ecosystems"GAKUTO International Series, Mathematical Sciences and Applications. Vol.12. 65-74 (1999)

[Publications] T. Ooura: "A robust double exponential formula for Fourier-type integrals"J. Comput. Appl. Math.. 112巻・1/2号. 229-241 (1999)

[Publications] K. Itakura: "An error analysis of streaklines as curves"Japan Journal of Industrial and Applied Mathematics. 16. 1-23 (1999)

[Publications] A. Suzuki: "Numerical solution of an ansteady earth's mantle convection problem by a stabilized finite element method"Theoretical and Applied Mechanics. 48. 371-378 (1999)

[Publications] M. Tabata: "A finite element analysis of a linearized problem of the Navier-Stokes equations with surface tention"SIAM Journal on Numerical Analysis. (to appear).

[Publications] M. T. Nakao: "Numerical verifications of eigenvalues of second-order elliptic operators"Japan Journal of Industrial and Applied Mathematics. 16. 307-320 (1999)

[Publications] K. Nagatou: "An approach to the numerical verification of solutions for nonlinear elliptic problems with local uniqueness"Numerical Functional Analysis and Optimization. 20. 543-565 (1999)

[Publications] Y. Watanabe: "A numerical verification method of solutions for the Navier-Stokes equations"Reliable Computing. 5. 347-357 (1999)

[Publications] T. Kako: "Numerical simulation of wave propagation phenomena in vocal tract and domain decomposition method"Domain decomposition method in science and engineering Proceeding of the 11th International Conference on Domain Decomposition Methods in Greenwich, UK. 267-269 (1999)

[Publications] F. Chiba: "Stability and error analyses by energy estimate for Newmark's method"Reserch Report NIFS-PRO Series. NIFS-PRO-40. 82-91 (1999)

[Publications] H. Suyari: "Information theoritical approach to the storage capacity of neural networks with binary weights"Phys. Rev. E,. 6・4. 4576-4579 (1999)

[Publications] H. Suyari: "Storage capacity of neural networks with binary weights using the minimum distance between input patterns"Proceedings of International Joint Conference on Neural Networks (IJCNN), Washington D.C.. 62-62 (1999)

[Publications] H. Imai: "Motion of Spirals by Crystalline Curvature"Mathematial Modelling and Numerical Analysis. 33・4. 797-806 (1999)

[Publications] H. Imai: "On Numerical Simulation of Partial Differential Equations in Infinite Precision"Advances in Mathematical Sciences and Applications. 9・2. 1007-1016 (1999)

[Publications] H. Imai: "A Crystalline Motion of Spiral-Shaped Curves with Symmety"Journal of Mathematical Analysis and Applications. 240・1. 115-127 (1999)

[Publications] N. Ishimura: "Nonexistence of monotonic solutions of some third order ODE relative to the Kuramoto-Sivashinsky equation"Tiwanese Journal of mathematics. (to appear). (2000)

[Publications] T. Hanada: "Numerical analysis of Eguchi-Oki-Matsumura equations"GAKUTO International Series, Mathematical Sciences and Applications, Advances in numerical mathematics in Japan and China. 12. 213-222 (1999)

河原田秀夫千葉大学, 工学部, 教授 (90010793)