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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.

涡旋法、薄层元法、小波法、有限差分法的研究取得了一定的进展。冈本发表了一篇关于基本解决方法的调查论文。在冈本的指导下，小林先生开发了一种计算最小曲面的新算法。F.Sasaki考虑了小波在积分方程中的新应用，其中传统的小波由于积分方程的非局域性而难以应用。murota和S.Iwata发展了混合矩阵的统一理论。他们编写了一个程序来计算混合矩阵的组合标准形式，并将其通过互联网提供。杉原先生考虑了基本解方法的理论背景。特别地，他提出了一种在三维域内定位奇异点的新方法。他还将双指数变换应用于函数逼近的Sinc方法。他的结果表明，在Sinc方法中，双指数变换是最优阶的。Y.Iso考虑了逆散射问题的一种数值方法。他说明了某高精度数值软件是非常有效的。池田对反应扩散方程的并行计算进行了数值实验。他澄清了并行计算中一些基本算法的理论背景，这些算法只是启发式地推导出来的。