粒子输运问题奇异积分方程的数值解与情形特征函数的部分范围完备性

IF 0.7 4区工程技术 Q3 MATHEMATICS, APPLIED

Journal of Computational and Theoretical Transport Pub Date : 2020-11-09 DOI:10.1080/23324309.2020.1819329

D. Sahni, R. G. Tureci, A. Z. Bozkır

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引用次数: 3

摘要

摘要研究了粒子输运理论奇异积分方程(SIE)的数值解。通过标准离散化处理将其转化为矩阵方程。发现该矩阵是高度病态的，可以用奇异值分解(SVD)方法求解。人们期望在部分值域上展开得到的矩阵不是病态的。我们发现这是不正确的，虽然他们的不良条件是一个数量级小于那些全范围或半范围。解释了这一现象的原因。

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Partial Range Completeness of Case Eigenfunctions and Numerical Solution of Singular Integral Equations of Particle Transport Problems

Abstract We study numerical solution of Singular Integral Equations (SIE) of particle transport theory. We convert them into matrix equations by standard discretization process. It is found that the matrices are highly ill-conditioned and can be solved by Singular Value Decomposition (SVD) method. One expects that matrices resulting from expansions over Partial Range will not be ill-conditioned. We find this is not true though their ill-conditioning is an order of magnitude less than those of full or half range. Reasons for this phenomenon are explained.

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来源期刊

Journal of Computational and Theoretical Transport Mathematics-Mathematical Physics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Emphasizing computational methods and theoretical studies, this unique journal invites articles on neutral-particle transport, kinetic theory, radiative transfer, charged-particle transport, and macroscopic transport phenomena. In addition, the journal encourages articles on uncertainty quantification related to these fields. Offering a range of information and research methodologies unavailable elsewhere, Journal of Computational and Theoretical Transport brings together closely related mathematical concepts and techniques to encourage a productive, interdisciplinary exchange of ideas.