Grant-in-Aid for Scientific Research (A).
|Allocation Type||Single-year Grants|
General mathematics (including Probability theory/Statistical mathematics)
|Research Institution||The University of Tokushima|
IMAI Hitoshi The University of Tokushima, Faculty of Engineering, Professor, 工学部, 教授 (80203298)
TOMOEDA Kenji Osaka Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (60033916)
TABATA Masahisa Kyushu University, Faculty of Mathematics, Professor, 大学院・数理学研究院, 教授 (30093272)
IKEDA Tsutomu Ryukoku University, Faculty of Science and Technology, Professor, 理工学部, 教授 (50151296)
NISHIDA Takaaki Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70026110)
NAKAO Mitsuhiro Kyushu University, Faculty of Mathematics, Professor, 大学院・数理学研究院, 教授 (10136418)
|Project Period (FY)
1998 – 2000
Completed(Fiscal Year 2000)
|Budget Amount *help
¥26,900,000 (Direct Cost : ¥26,900,000)
Fiscal Year 2000 : ¥5,400,000 (Direct Cost : ¥5,400,000)
Fiscal Year 1999 : ¥5,300,000 (Direct Cost : ¥5,300,000)
Fiscal Year 1998 : ¥16,200,000 (Direct Cost : ¥16,200,000)
|Keywords||multiple precision / parallel computing / PVM / simulation / spectral method / verification / arbitrary / infinite / 計算機支援 / 任意精度 / 無限精度 / 高精度|
In the term of the project (three years) many results were obtained. Important results are shown as follows.
1. Building of the parallel computing environment.
High-performance workstations were purchased and connected by the high-speed network. PVM (Parallel Virtual Machine) was implemented on these workstations. Thus, the parallel computing environment was built at Imai's laboratory at Tokusima University.
2. Development of Infinite Precision Numerical Simulation.
Errors in numerical simulations originate from truncation errors in discretization and rounding errors. Infinite Precision Numerical Simulation was developed by combining the spectral (collocation) method and multiple precision arithmetic. The spectral (collocation) method is used for the control of truncation errors. Multiple precision arithmetic is used for the control of rounding errors. The method was applied to PDE systems with smooth solutions. The feature of the method, i.e. arbitrary reduction of errors, was observed. In a one-dimensional boundary value problem errors were approximately 10^<-2300>. This is incredible compared with results by other numerical methods.
3. Development of the library and its release.
The library for Infinite Precision Numerical Simulation was developed. The subroutine of Gauss elimination in multiple precision arithmetic was developed. Its parallelization was performed by using PVM.The library was released by up-loading the report of the research project on Imai's home page.
4. Related results.
Many related results were obtained as for development of infinite magnifying in visualization, development of parallel computing by using domain decomposition, basic research and application of Infinite Precision Numerical Simulation to inverse problems, free boundary problems and fluid mechanics, research on verification.