Fast Implementation of the Boundary Element Method and its Application to Inverse Problems

边界元法的快速实现及其在反问题中的应用

基本信息

项目摘要

1) Direct simulation of large amplitude standing waves using the boundary element methodWe developed a method using the two-dimensional boundary element method for the time dependent direct simulation of the free surface of liquids, and succeeded in the direct simulation of large amplitude standing waves, which was considered to be difficult.2) Inverse ProblemWe developed efficient direct methods for the inverse problem of source term identification of the three-dimensional Poisson equation, which is applied to MEG etc. Depending on whether the source is 1) relatively uniformly distributed in the domain, 2) concentrated near the boundary of the domain, infinite series of the 1) low-order moments, 2) high-order moments of the multipole expansion of the field are used in order to obtain reconstruction formulae concerning the position of the projection of the source on to the 1) xy-plane, 2) Riemann sphere.3) Iterative methods on singular systemsWe analyzed the behavior of Krylov subspace … More iterative methods on least-squares problems whose coefficient matrices are singular. Namely, we derived necessary and sufficient conditions for the CR (Conjugate Residual), GCR(k) (Generalized Conjugate Residual) and GMRES (Generalized Minimal Residual) methods to give a least-square solution without break-down. The methodology is to decompose the algorithms in to the range of the coefficient matrix and its orthogonal complement.We also developed a method of applying the GMRES method after preconditioning by incomplete QR decomposition, for (over-determined) least-squares problems.4) Iterative methods for eigenvalue problemsWe derived necessary and sufficient conditions for a solution to exist to the correction equation of the Jacobi-Davidson method, clarified the relation between the subspace expanded by such a solution and the invariant space of the coefficient matrix, and proposed a method for generating efficient starting vectors for the method. We also proposed methods for the validated numerics of the method. Less
1)用边界元法直接模拟大振幅驻波本文发展了一种用二维边界元法直接模拟与时间有关的液体自由表面的方法,并成功地直接模拟了大振幅驻波。这被认为是困难的。反问题我们发展了三维Poisson方程源项识别反问题的有效直接方法,其应用于MEG等。取决于源是否1)相对均匀地分布在域中,2)集中在域的边界附近,1)低阶矩的无穷级数,2)使用场的多极展开的高阶矩以获得关于源在xy平面上的投影位置的重建公式,2)Riemann球; 3)奇异系统的迭代方法我们分析了Krylov子空间的性质 ...更多信息 系数矩阵奇异的最小二乘问题的迭代方法。即给出了CR(Conjugate Residual)、GCR(k)(Generalized Conjugate Residual)和GMRES(Generalized Minimum Residual)方法给出无故障最小二乘解的充要条件。该方法是将算法分解到系数矩阵及其正交补的范围内,并提出了一种在不完全QR分解预处理后应用GMRES方法的方法,(超定)最小二乘问题。4)特征值问题的迭代方法我们导出了Jacobi-Davidson方法的修正方程有解的充要条件,阐明了该解所展开的子空间与系数矩阵的不变空间之间的关系,并提出了一种有效的初始向量生成方法。我们还提出了方法的验证数值的方法。少

项目成果

期刊论文数量(80)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Ken Hayami: "A panel clustering method for 3-D elastostatics using spherical harmonics"Integral Methods in Science and Engineering (Chapman & Hall/CRC). 179-184 (2000)
Ken Hayami:“使用球谐函数进行 3-D 弹性静力学的面板聚类方法”科学与工程中的积分方法(查普曼
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伊藤 徳史: "不完全QR-GMRES(k)法による線形最小二乗問題の解法"情報処理学会第65回全国大会講演論文集. 1-117-1-118 (2003)
Tokushi Ito:“使用不完全 QR-GMRES(k) 方法解决线性最小二乘问题”第 65 届日本信息处理学会全国会议论文集 1-117-1-118 (2003)。
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今井 聡: "Jacobi-Davidson法における初期ベクトルの改良"日本応用数理学会2001年度年会予稿集. 276-277 (2001)
Satoshi Imai:“雅可比-戴维森方法中初始向量的改进”日本应用数学学会 2001 年年会记录 276-277 (2001)。
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Hayami, K.: "On the convergence of the conjugate residual method on singular systems"Proceedings of the 2000 Annual Meeting of the Japan Society for Industrial and Applied Mathematics. 58-59 (2000)
Hayami, K.:“论奇异系统上共轭残差法的收敛性”日本工业与应用数学学会 2000 年年会论文集。
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濱野健二: "大振幅定在波の境界要素法による直接シミュレーション"数理解析研究所講究録(非線形波動現象のメカニズムと数理). 1209. 105-114 (2001)
Kenji Hamano:“使用边界元法直接模拟大振幅驻波”数学分析研究所的Kokyuroku(非线性波现象的机制和数学)1209.105-114(2001)。
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HAYAMI Ken其他文献

HAYAMI Ken的其他文献

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{{ truncateString('HAYAMI Ken', 18)}}的其他基金

Iterative Methods for Least Squares Problems and their Application to Inverse Problems
最小二乘问题的迭代方法及其在反问题中的应用
  • 批准号:
    24560082
  • 财政年份:
    2012
  • 资助金额:
    $ 1.73万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
The Solution of Least Squares Problems Using Krylov Subspace Methods
用Krylov子空间方法求解最小二乘问题
  • 批准号:
    21560072
  • 财政年份:
    2009
  • 资助金额:
    $ 1.73万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
The Research on Making the Boundary Element Method Highly Accurate and Efficient
边界元法高精度高效化的研究
  • 批准号:
    06650073
  • 财政年份:
    1994
  • 资助金额:
    $ 1.73万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)

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