Co-operative Research on Numerical Analysis of Partial Differential Equations Applied to High Technology.

偏微分方程数值分析应用于高科技的合作研究。

• 批准号: 04305013
• 负责人: ONISHI Kazuei
• 金额: $ 4.22万
• 依托单位: Science University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1992
• 资助国家: 日本
• 起止时间: 1992 至 1994
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-04305013/
• 关键词: Partial differential equations; Approximation theory; Numerical analysis; Computational mechanics; Finite element method; Boundary element method; Integral equations; Inverse problems; 代用電荷法; 自由境界問題

The research aimed at strengthening and rearranging application-oriented basic theories in the numerical solutions of partial differential equations. It also aimed at promoting transfer of the theories to modern high technology in industries. The objective was emphasized about the following issues --- and some corresponding remarkable results are obtained :1. New methodologies in numerical solution technique for partial differential equations should be proposed from point of view on their applications to high technology. --- New finite element scheme in computational fluid dynamics, mathematical elucidation of chrge simulation method.2. Re-examination of mathematical models required in industries for new development of high technology should be taken from point of view on mathematical analysis and computation.--- Highly accurate computation in boundary element technique, new applications of integral equation methods to highly nonlinear mechanics and inverse problems.Integration in co-operative research work in interdisciplinary areas in science and engineering should be accelerated. --- Several symposiums, forums, and workshops dedicated.

该研究旨在在部分微分方程的数值解决方案中加强和重新安排面向应用程序的基本理论。它还旨在促进将理论转移到行业现代高科技的转移。强调了以下问题的目的 - 获得了一些相应的显着结果：1。对于部分微分方程的数值解决方案技术中的新方法，应从其对高科技应用的视角提出。 ---计算流体动力学中的新有限元方案，CHRGE模拟方法的数学阐明2。在数学分析和计算的角度，应采取重新审查高科技开发所需的数学模型。 ---专门的几个研讨会，论坛和研讨会。

项目成果

Hirose,S.,Kitahara,M.: "Ultrasonic scattering analysis to characterize nonlinear behavior of material interfaces." Nondestructive Testing and Evaluation. 8-9. 405-416 (1992)

Hirose,S.，Kitahara,M.：“超声散射分析来表征材料界面的非线性行为。”

友枝 謙二,三村 昌泰: "Numerical computation for through porous media" 物性研だより物性研短期研究会「パーコレーションの理論と応用」. 32-3. 70-71 (1992)

Kenji Tomoeda、Masayasu Mimura：“多孔介质的数值计算”来自固体物理研究所短期研究小组的通讯“渗流理论与应用”32-71 (1992)。

今井仁司・周偉東・河原田秀夫 沢栗利男・名取亮: "不適切な問題に対する適用可能な数値解法の検討" 数理解析研究所講究録. 102-112 (1993)

Hitoshi Imai、Weidong Zhou、Hideo Kawarada、Toshio Sawakuri 和 Ryo Natori：“对不适当问题的适用数值解决方案的研究”数学分析研究所的 Kokyuroku 102-112 (1993)。

岡本 久,桂田 祐史: "ポテンシャル問題の高速解法" 応用数理. 2. 2-20 (1992)

Hisashi Okamoto、Yuji Katsurada：“潜在问题的快速解决”应用数学。2. 2-20 (1992)

久保 司郎,大路 清嗣,桑山 真二郎: "特異値分解を用いた境界値逆問題の解析とその適切化" 日本機械学会講演文集. 920-78A. 1-3 (1992)

Shiro Kubo、Kiyoshi Oji、Shinjiro Kuwayama：“使用奇异值分解的边值逆问题的分析和优化”日本机械工程师学会会议记录 920-78A (1992)。