Updating of Poisson Solvers

泊松解算器的更新

• 批准号: 10554003
• 负责人: USHIJIMA Teruo
• 金额: $ 8.9万
• 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: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-10554003/
• 关键词: Poisson solver; fundamental solution method; Finite element method; Numerical conformal mapping; Radiation and scattering problems in infinite domains; Odd and even dimensional Radon transforms; Asymmetric Abel inversion; Numerical methods for Helm

1. Main Results Obtained in the Joint Works around the Head Investigator :In the computatioin of two dimensional perfect fluid around an air foil through finite element method, setting a sufficiently large disc containing the air foil, let a doubly connected region, which is the intersection of the disc and the complement of the air foil, be our computational domain. Setting a transparent boundary condition on the circular boundary of the computational domain. Setting a transparent boundary condition on the circular boundary of the computational domain, we execute finite element numerical computations for discretized Laplace problems in the domain. To solve the discretized problems, an FEM-CSM (finite Element Method -- Charge Simulation Method) combined method for 2D exterior Laplace problems is proposed and mathematically justified. In this combined method transparent boundary condition is approximated through charge simulation method. For an FSM (Fundamental Solution Method) approxim … More ate problem for Helmholtz equation in the exterior domain of a disc, a unique solvability theorem and an error estimate theorem are obtained in the case of equi-distant equally phased arrangement of source points and collocation points.2. Remarkable Progress Obtained in the Works by Investigators :(1) Representations of the inversions of the odd and even dimensional Radon transforms and numerical reconstruction procedures based on them (by J. Watanabe)(2) Neural network calculation in asymmetric Abel inversion (by T. Takeda and M Fukuhara)(3) Finite element numerical method based on the domain decomposition method and fictitious domain method applied to radiation and scattering problem in unbounded region (by T. Kako).(4) fundamental research for numerical simulation of dynamical systems generated by delay differential equations (by T. Koto).(5) A free boundary problem related to eigenvalue problems for a class of elliptic partial differential operators (by I. Ohnishi).(6) Theoretical study on reaction-diffusion equations and their singular limits describing the growth of screw dislocation on the crystal surface (by K. Nakamura).(7) Finite element computations for 3D exterior Helmholtz problem (by D. Koyama).(8) A parallel computation code for 3D numerical simulation of Earth's mantle convection (by M. Tabata).(9) Proposal of a method of numerical conformal mappings of unbounded multiply-connected domains onto canonical slit domains using the charge simulation method, and confirmation of its effectiveness by numerical experiments (by K. Amano).(10) A theoretical study on the 1-dimensional Poisson solvers based on sinc functions (by M. Sugihara).(11) Mathematical foundation of residual cutting method (by T. Takahashi).(12)Role of Poisson solvers in bio-informatics (by S. Ihara).(13) Derivation of basic system of equations for multi phase flow appearing in the structure formation in nanotechnology (by H. Yasuda). Less

1.主要成果：在二维理想流体绕翼型的有限元计算中，设置一个足够大的包含翼型的圆盘，以圆盘与翼型的补面相交的双连通区域作为计算区域。在计算域的圆形边界上设置透明边界条件。在计算域的圆形边界上设置透明边界条件，对域内离散的拉普拉斯问题进行有限元数值计算。为了解决离散化问题，提出了二维外部拉普拉斯问题的FEM-CSM（有限元法-电荷模拟法）组合方法，并进行了数学证明。该方法采用模拟电荷法近似透明边界条件。对于FSM（基本解方法）近似， ...更多信息 在源点和配置点等距等相位布置的情况下，得到了圆片外区域上Helmholtz方程的解的唯一性定理和误差估计定理.研究者在工作中取得的显著进展：（1）奇、偶维Radon变换的反演表示及基于它们的数值重建方法（J. Watanabe）;（2）非对称Abel反演的神经网络计算（T.（3）基于区域分解法和虚拟区域法的有限元数值方法在无界区域辐射和散射问题中的应用（T。Kako）。(4)延迟微分方程生成的动力系统数值模拟的基础研究（T. Koto）。(5)一类椭圆型偏微分算子特征值问题的自由边值问题（I。大西）。(6)对描述晶体表面螺型位错生长的反应扩散方程及其奇异极限进行了理论研究（K。中村）。(7)三维Helmholtz外问题的有限元计算（D. Koyama）。(8)本文介绍了一个用于地幔对流三维数值模拟的并行计算程序。Tabata）。(9)提出了一种用电荷模拟方法将无界多连通域数值共形映射到正则狭缝域的方法，并通过数值实验验证了该方法的有效性（K. Amano）。(10)本文对基于sinc函数的一维Poisson求解器进行了理论研究。Sugihara）。(11)余割法的数学基础（T. Takahashi）。（12）泊松求解器在生物信息学中的作用（S.伊原）。(13)推导了纳米技术中结构形成过程中出现的多相流基本方程组。Yasuda）。少

项目成果

Tosiko Ogiwara, Ken-Ichi Bakamura: "Asymptotic behavior of solutions to a model of spiral crystal growth"京都大学数理解析研究所講究録. (to appear). (2002)

Tosiko Ogiwara、Ken-Ichi Bakamura：“螺旋晶体生长模型解的渐近行为”京都大学数学科学研究所 Kokyuroku（待发表）。

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

S.-L.Zhang、Y.Oyanagi 和 M.Sugihara：“奇异和不一致线性系统上 Orthomin (k) 收敛的必要和充分条件”数值数学。

M.Sugihara: "Sinc-Galekin 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).

M.Sugihara：“两点边值问题的双指数变换的Sinc-Galekin法”第五届中日数值数学研讨会论文集。

KAKO,Takashi,KANO,Tomotoshi,LIU,Xiao-Jin and YAMASHITA,Takehiko: "Domain decomposition method applied to radiation problems"Proceedings of 12th DDM International Conference. (2001 掲載予定).

KAKO、Takashi、KANO、Tomotoshi、LIU、Xiao-Jin 和 YAMASHITA、Takehiko：“应用于辐射问题的域分解方法”第 12 届 DDM 国际会议论文集（将于 2001 年出版）。

馬笑峰,竹田辰興: "ニューラルネットワークによるCT像再構成法"日本応用数理学会論文誌. 第10巻、第2号. 145-161 (2000)

马绍峰，武田龙兴：“使用神经网络的CT图像重建方法”日本应用数学学会学报第10卷第2.145-161期（2000年）。