Project/Area Number  10640108 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  The University of ElectroCommunications 
Principal Investigator 
USHIJIMA Teruo THE UNIVERSITY OF ELECTROCOMMUNICATIONS, FACULTY OF ELECTROCOMMUNICATIONS, PROFESSOR, 電気通信学部, 教授 (10012410)

CoInvestigator(Kenkyūbuntansha) 
FUKUHARA Makoto THE UNIVERSITY OF ELECTROCOMMUNICATIONS, FACULTY OF ELECTROCOMMUNICATIONS, RESEARCH ASSOCIATE, 電気通信学部, 助手 (60272754)
KOYAMA Daisuke THE UNIVERSITY OF ELECTROCOMMUNICATIONS, FACULTY OF ELECTROCOMMUNICATIONS, ASSOCIATE PROFESSOR, 電気通信学部, 助手 (60251708)
KATO Toshiyuki THE UNIVERSITY OF ELECTROCOMMUNICATIONS, FACULTY OF ELECTROCOMMUNICATIONS, ASSOCIATE PROFESSOR, 電気通信学部, 助教授 (30234793)
KATO Takashi THE UNIVERSITY OF ELECTROCOMMUNICATIONS, FACULTY OF ELECTROCOMMUNICATIONS, PROFESSOR, 電気通信学部, 教授 (30012488)
TAKEDA Tatsunoki THE UNIVERSITY OF ELECTROCOMMUNICATIONS, FACULTY OF ELECTROCOMMUNICATIONS, PROFESSOR, 電気通信学部, 教授 (60272746)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,400,000 (Direct Cost : ¥2,400,000)
Fiscal Year 1999 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)

Keywords  Steklov operator / Finite ElementCharge Simulation combined method / Finite ElementFundamental Solution combined method / 2 dimensional exterior Laplace problem / 2 dimensional exterior Helmholtz problem / Neural network / RungeKutta method / Newmark's method / スチェクロス作用素 / 有限要素代用電荷結合解法 / 有限要素基本解近似結合解法 / 二次元外部ラプラス問題 / 二次元外部ヘルムホルツ問題 / ニューラルネットワーク / ルンゲクッタ法 / ニューマーク法 / 有限要素法 / 代用電荷法 / 翼の等角写像 / 二次元ラプラス外部問題 / ヘルムホルツ方程式 
Research Abstract 
1. Main Results Obtained in the Joint Works around the Head Investigator : (1) Discretization method through charge simulation method for Steklov operator associated with Laplace problems in exterior domain of a disc. An FEMCSM (Finite Element Method  Charge Simulation Method) combined method for 2D exterior Laplace problems was proposed in 1998 and its mathematical analysis has been studied during whole the term of project. Relation between continuous and discrete fourier coefficients, which is a key for the study, has been investigated. (2) Confirmation of the effectiveness of the FEMFSM combined method through numerical computation (jointly with Masuda, S.). (3) Determination of the conformal mapping of wing through precise finite element computation for the potential function and stream function. (4) Proposal of the fundamental solution method (FSM, in short) for the determination of Steklov operator associated with the reduced wave problems in exterior domain of a disc. 2. Remarkabl
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e Progress Obtained in the Works by Investigators : (1) Numerical method for partial differential equations through neural network. Boundary condition fitting with the use of shape factor in the form of approximate function. Neural network solver for MHD equilibrium equation and NapierStokes equation. Acceleration of the neural net solution method with the use of GaussNewton method. (Obtained by Takeda and Fukuhara) (2) An iterative method for Helmholtz equation in domain decomposition computation. Numerical analysis and computation of the wave propagation in a bounded domain with open boundary portion connected with exterior infinite region. Proof of stability and convergence for Newmark's method for second order problem (obtained by Kako, T.). (3) Stability analysis for RungeKutta method through linear system theory. Stability analysis for RungeKutta method applied to delaydifferential equations (obtained by Koto). (4) Mathematical justification for a wave equation method solving exterior Helmholtz problems. Proposal and justification of a new artificial boundary condition to the wave equation solver for exterior Helmholtz problem (obtained by Koyama). 3. Keeping the UECNASeminar (University of ElectroCommunications Numerical Analysis Seminar). In each academic year of 1998 and 1999, 14 seminars were held in the Friday morning, generally. Within seminars, talks given by Professor Kamitani, A. of Yamagata University, Professor Sakajo, T. of Nagoya University, Professor Yamamoto, N. of then Kyushu university, Professor Matsuo, T. of Nagoya University, Professor Kanayama, H. of Kyushu University were supported by this grant. In addition to these regular seminar, special oneday and twoday workshops were held to discuss the subject of the project and related topics. Less
