抄録
Offer Organization: Japan Society for the Promotion of Science, System Name: Grants-in-Aid for Scientific Research, Category: Grant-in-Aid for Scientific Research (C), Fund Type: -, Overall Grant Amount: - (direct: 2400000, indirect: -)
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 FEM-CSM (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 FEM-FSM 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. Remarkable 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 Napier-Stokes equation. Acceleration of the neural net solution method with the use of Gauss-Newton 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 Runge-Kutta method through linear system theory. Stability analysis for Runge-Kutta method applied to delay-differential 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 UEC-NA-Seminar (University of Electro-Communications 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 one-day and two-day workshops were held to discuss the subject of the project and related topics.