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On the research and development of fast solvers arising in scientific computation

科学计算中快速求解器的研究与开发

基本信息

批准号：
09554003
负责人：
OKAMOTO Hisashi
金额：
$ 7.42万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09554003/
关键词：
Fast summation method fundamental solution method spectral method high precision computation ill-posed problem thin layer element method wavelet finite difference method 渦法逆問題精度保証計算領域分割法

项目摘要

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.

在涡量法、薄层单元法、小波、有限差分法等方面的研究取得了进展。冈本发表了一篇关于基本解方法的调查论文。小林先生在冈本的指导下开发了一种计算极小曲面的新算法。F.Sasaki考虑了小波在积分方程中的一种新的应用，其中由于积分方程的非局部性，传统的小波很难应用。K.Murota和岩田发展了混合矩阵的统一理论。他们编写了一个计算混合矩阵的组合标准形的程序，并通过互联网提供。M.Sugihara考虑基本解方法的理论背景。特别地，他提出了一种新的方法来定位在三维域中的奇点。他还适用于双指数变换的Sinc方法的功能近似。他的结果表明，双指数变换是Sinc方法中的最佳阶。Iso研究了逆散射问题的一种数值方法。他表明，某种高精度数值软件是非常有效的。池田作了反应扩散方程并行计算的数值实验。他澄清了一些理论背景的基本算法在并行计算，]这已经只是推导。