1998 Fiscal Year Final Research Report Summary
On the research and development of fast solvers arising in scientific computation
| Project/Area Number |
09554003
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 展開研究 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyoto University |
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Principal Investigator |
OKAMOTO Hisashi KYOTO UNIVERSITY,Research Istitute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (40143359)
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| Co-Investigator(Kenkyū-buntansha) |
SASAKI Fumio Kajima Corporation, Information Processing Center, System Engineering Section, C, 情報システム部, 主査
TAKANO Shinichiro Ohbayashi Corporation Technical Research Institute, Senior researcher, 技術研究所, 主任研究員
SUGIHARA Masaaki Nagoya University School of Engineering, Professor, 大学院・工学研究科, 教授 (80154483)
MORI Masatake KYOTO UNIVERSITY,Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (20010936)
MUROTA Kazuo KYOTO UNIVERSITY,Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (50134466)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Fast summation method / fundamental solution method / spectral method / high precision computation / ill-posed problem / thin layer element method / wavelet / finite difference method |
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| Research Abstract |
Progress is made in the study of vortex method, thin layer element method, wavelet, finite difference method. Okamoto published a survey paper on the fundamental solution method. Mr. K.Kobayashi develops, under the guidance of Okamoto, a new algorithm for computing the minimal surfaces. F.Sasaki considers a new application of wavelets to integral equations, in which the conventional wavelets are difficult to be applied because of the nonlocality of the integral equations. K.Murota and S.Iwata develop a unified theory for the mixed matrices. They write a program to compute the combinatorial canonical form of the mixed matrices and made it available through internet. M.Sugihara considers theoretical background of the fundamental solution method. In particular he proposes a new method of locating the singularities in three-dimensional domain. He also applies the double exponential transform to the Sinc method of functional approximation. His results show that the double exponential transform is of the optimal order in the Sinc method. Y.Iso considers a numerical method for inverse scattering problem. He shows that a certain high precision numerical software is very effective. T.Ikeda performs numerical experiments of the parallel computation for the reaction-diffusion equation. He clarifies some of the theoretical background of basic algorithms in the parallel computation, ] which has been only heuristically derived.
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