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首页> 外文学位 >Explicitly restarted Arnoldi's method for Monte Carlo nuclear criticality calculations.
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Explicitly restarted Arnoldi's method for Monte Carlo nuclear criticality calculations.

机译：明确重启了阿诺迪的蒙特卡洛核临界计算方法。

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摘要

A Monte Carlo implementation of explicitly restarted Arnoldi's method is developed for estimating eigenvalues and eigenvectors of the transport-fission operator in the Boltzmann transport equation. Arnoldi's method is an improvement over the power method which has been used for decades. Arnoldi's method can estimate multiple eigenvalues by orthogonalising the resulting fission sources from the application of the transport-fission operator. As part of implementing Arnoldi's method, a solution to the physically impossible---but mathematically real---negative fission sources is developed. The fission source is discretized using a first order accurate spatial approximation to allow for orthogonalization and normalization of the fission source required for Arnoldi's method. The eigenvalue estimates from Arnoldi's method are compared with published results for homogeneous, one-dimensional geometries, and it is found that the eigenvalue and eigenvector estimates are accurate within statistical uncertainty.;The discretization of the fission sources creates an error in the eigenvalue estimates. A second order accurate spatial approximation is created to reduce the error in eigenvalue estimates. An inexact application of the transport-fission operator is also investigated to reduce the computational expense of estimating the eigenvalues and eigenvectors.;The convergence of the fission source and eigenvalue in Arnoldi's method is analysed and compared with the power method. Arnoldi's method is superior to the power method for convergence of the fission source and eigenvalue because both converge nearly instantly for Arnoldi's method while the power method may require hundreds of iterations to converge. This is shown using both homogeneous and heterogeneous one-dimensional geometries with dominance ratios close to 1.
机译：开发了明确重启的Arnoldi方法的蒙特卡洛实现方法，用于估计玻耳兹曼输运方程中运移裂变算符的特征值和特征向量。 Arnoldi的方法是对几十年来使用的幂方法的改进。 Arnoldi的方法可以通过从运输裂变算子的应用中正交化所得裂变源来估计多个特征值。作为实施Arnoldi方法的一部分，开发了一种解决物理上不可能的（但在数学上是实际的）负裂变源的方法。使用一阶精确空间近似离散化裂变源，以实现Arnoldi方法所需的裂变源的正交化和归一化。将Arnoldi方法的特征值估计与已发表的均匀一维几何结构的结果进行了比较，发现特征值和特征向量估计在统计不确定性内是准确的。裂变源的离散化在特征值估计中产生了误差。创建二阶准确的空间近似值以减少特征值估计中的误差。还研究了运输裂变算子的不精确应用，以减少估计特征值和特征向量的计算量。；分析了Arnoldi方法中裂变源和特征值的收敛性，并与幂方法进行了比较。对于裂变源和特征值的收敛，Arnoldi的方法优于幂方法，因为两者对于Arnoldi的方法都几乎立即收敛，而幂方法可能需要数百次迭代才能收敛。使用均一和均一优势比接近1的同构和异构一维几何体都可以看到这一点。

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  • 作者

    Conlin, Jeremy Lloyd.;

  • 作者单位

    University of Michigan.;

  • 授予单位 University of Michigan.;
  • 学科 Engineering Nuclear.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 115 p.
  • 总页数 115
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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