Study on non-standard finite element approximation methods for partial differential equations

偏微分方程非标准有限元逼近方法研究

• 批准号: 11440027
• 负责人: KAKO Takashi
• 金额: $ 8.7万
• 依托单位: The University of Electro-Communications
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-11440027/
• 关键词: Finite element method; Radiation and scattering problem; Domain decomposition method; Drichlet to Neumann mapping; Fundamental solution method; Earth mantle current; Neutral net computation; Validated computation; ディリクレ・ノイマン写像; 亀裂進展問題; 四面体一次要素 /

The following results have been obtained for the non-standard finite element method (FEM) and related problems. The head investigator T. Kako studied the wave propagation in the I exterior unbounded region finding the non-standard finite element approximation method j for a non-local Dirichlet to Neumann mapping, and developed an effective method for 2D radiation problem with high wave number. As an application of the method, it has become possible to compute the formant curve close to the one for the real vowels. He developed the numerical method for the coupling problem between the acoustic field and the structure like shell. He also made clear the importance of the essential Spectrum of the operator in its FEM. The followings are the results by investigators. T. Ushijima studied the fundamental solution method for the 2D reduced wave problem and obtained the convergence and the error estimation. K. Houlka developed the Freeform+ project. H. Kawakawa studied the oil adherence and pen … More etration phenomena on the seashore and obtained its mathematical model and did numerical simulations with various applications.F. Kikuchi developed a new FEM for the plate-bending problem with several numerical examples and studied the efficiency of the Nedelec edge element. D. Koyama studied FEM for the 3D exterior Helmholtz problem combining the fictitious domain method and the Schwarz alternative method. T. Takeda and M. Fukuhara developed the structured neural network method for partial differential equations. M. Tabata found the new FEM scheme for earth mantle convection problem with error estimation. S. -L. Zhang studied various conjugate gradient type method for linear equations. T. Miyoshi found a criterion to determine the direction of a crack extension. M. Nakao and N. Yamamoto studied the validated numerical method for FEM computation and developed the method to evaluate the approximation property of FEM with validation by reducing the problem to the generalized matrix eigenvalue problem. Less

对非标准有限元法及相关问题进行了研究，得到了以下结果。首席调查员T。Kako研究了波在I外无界区域中的传播，找到了非局部Dirichlet到Neumann映射的非标准有限元逼近方法j，并发展了一种求解高波数二维辐射问题的有效方法。作为该方法的一个应用，计算出的共振峰曲线与真实的元音的共振峰曲线非常接近。他发展了声场与壳体等结构之间耦合问题的数值方法。他还阐明了算子的本质谱在其有限元中的重要性。以下是研究者的结果。T. Ushijima研究了二维约化波问题的基本解方法，得到了收敛性和误差估计。K. Houlka开发了Freeform+项目。H.川川研究了油的粘附性和笔 ...更多信息 分析了海岸带的渗透现象，建立了渗透的数学模型，并进行了数值模拟.菊池通过几个数值例子开发了一种新的板弯曲问题有限元方法，并研究了Nedelec边缘单元的效率。D. Koyama结合虚拟区域法和施瓦茨交替法研究了三维Helmholtz外问题的有限元法。T. Takeda和M. Fukuhara发展了偏微分方程的结构神经网络方法。M. Tabata提出了一种新的地幔对流问题的有限元格式，并给出了误差估计。S. -L.研究了线性方程组的各种共轭梯度型方法。T. Miyoshi发现了一个判断裂纹扩展方向的准则。M. Nakao和N. Yamamoto研究了有限元计算的有效数值方法，并通过将问题简化为广义矩阵特征值问题，发展了评估有限元逼近性能的方法。少

项目成果

Koyama,D.: "A time-dependent numerical algorithm for the Helmholtz equation"京都大学数理解析研究所講究録. 1145. 113-120 (2000)

Koyama, D.：“亥姆霍兹方程的时间相关数值算法”京都大学数学科学研究所 Kokyuroku。1145. 113-120 (2000)。

Zhang,S.-L.,Y.Oyanagi and Sugihara,M.: "Necessary and Sufficient Conditions for Convergence of Orthomin (K) on Singular and Inconsistent Linear Systems"Numerische Mathematik. 87-2. 391-405 (2000)

张S.-L.，Y.Oyanagi和Sugihara，M.：“奇异和不相容线性系统上Orthomin（K）收敛的充分必要条件”数值数学。

Nagatou K.,Yamamoto, N.and Nakao, M.T.: "An approach to the numerical verification of solutions for nonlinear elliptic problems with local uniqueness"Numerical Functional Analysis and Optimization. 20. 543-565 (1999)

Nagatou K.、Yamamoto, N. 和 Nakao, M.T.：“具有局部唯一性的非线性椭圆问题解的数值验证方法”数值泛函分析和优化。

Edited by T.Kako and T.Watanabe: "Proceedings of 1998-Workshop on MHD Computations "Study on Numerical Methods related to Plasma Confinement""National Institute for Fusion Science (NIFS). 211 (1999)

T.Kako和T.Watanabe编辑：“1998年论文集-MHD计算研讨会“与等离子体约束有关的数值方法的研究””国家融合科学研究所（NIFS）。

KAKO, T., NASIR, H.M.: "Essential spectrum and mixed type finite element method"Lecture Notes in Computational Science and Engineering, Proceedings of MSCOM. 19. 155-167 (2002)

KAKO, T.，NASIR, H.M.：“本质谱和混合型有限元法”计算科学与工程讲义，MSCOM 会议录。