Grant-in-Aid for Scientific Research (B)
|Allocation Type||Single-year Grants|
General mathematics (including Probability theory/Statistical mathematics)
|Research Institution||THE UNIVERSITY OF ELECTRO-COMMUNICATIONS|
USHIJIMA Teruo THE UNIVERSITY OF ELECTRO-COMMUNICATIONS, FACULTY OF ELECTRO-COMMUNICATIONS, PROFESSOR, 電気通信学部, 教授 (10012410)
SUGIHARA Masaaki NAGOYA UNIVERSITY, GRADUATE SCHOOL OF ENGINEERING, PROFESSOR, 大学院・工学研究科, 教授 (80154483)
AMANO Kaname EHIME UNIVERSITY, FACULTY OF ENGINEERING, PROFESSOR, 工学部, 教授 (80113512)
TABATA Masahisa KYUSHU UNIVERSITY, GRADUATE SHCOOL OF SCIENCES, PROFESSOR, 大学院・理学研究院, 教授 (30093272)
KAKO Takashi THE UNIVERSITY OF ELECTRO-COMMUNICATIONS, FACULTY OF ELECTRO-COMMUNICATIONS, PROFESSOR, 電気通信学部, 教授 (30012488)
TAKEDA Tatsuoki THE UNIVERSITY OF ELECTRO-COMMUNICATIONS, FACULTY OF ELECTRO-COMMUNICATIONS, PROFESSOR, 電気通信学部, 教授 (60272746)
安田 英典 三菱総合研究所, 総合安全研究センター, 研究部長
|Project Period (FY)
1998 – 2001
Completed(Fiscal Year 2001)
|Budget Amount *help
¥13,900,000 (Direct Cost : ¥13,900,000)
Fiscal Year 2001 : ¥3,500,000 (Direct Cost : ¥3,500,000)
Fiscal Year 2000 : ¥3,500,000 (Direct Cost : ¥3,500,000)
Fiscal Year 1999 : ¥3,400,000 (Direct Cost : ¥3,400,000)
Fiscal Year 1998 : ¥3,500,000 (Direct Cost : ¥3,500,000)
|Keywords||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 Helmholtz equations / 離散変分法 / ニューラルネットワーク計算 / ヘルムホルツ方程式 / 基本解近似法 / 地球マントル対流の有限要素計算 / データ同化問題 / ヘルマホルツ方程式 / 代用電荷近似法 / 数値等角写像法 / スチェクロフ境界双一次形式 / 二次元ポテンシャル流解析 / 翼外調和関数 / 代用電荷法 / 等角写像 / SINC関数近似 / 混層流|
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
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