A block Arnoldi method for the SPN equations

The simplified spherical harmonics equations are a useful approximation to the stationary neutron transport equation. The eigenvalue problem associated with them is a challenging problem from the computational point of view. In this work, we take advantage of the block structure of the involved matr...

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Bibliographic Details
Published inInternational journal of computer mathematics Vol. 97; no. 1-2; pp. 341 - 357
Main Authors Vidal-Ferràndiz, A., Carreño, A., Ginestar, D., Verdú, G.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.02.2020
Taylor & Francis Ltd
Subjects
block inverse-free preconditioned Arnoldi method
Computational efficiency
Computing time
Eigenvalues
Finite element analysis
Finite element method
Galerkin method
generalized Davidson method
Generalized eigenvalue problem
Iterative methods
Mathematical analysis
multilevel method
neutron transport
Nonlinear programming
Shape functions
Spherical harmonics
Transport equations
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Summary:The simplified spherical harmonics equations are a useful approximation to the stationary neutron transport equation. The eigenvalue problem associated with them is a challenging problem from the computational point of view. In this work, we take advantage of the block structure of the involved matrices to propose the block inverse-free preconditioned Arnoldi method as an efficient method to solve this eigenvalue problem. For the spatial discretization, a continuous Galerkin finite element method implemented with a matrix-free technique is used to keep reasonable memory demands. A multilevel initialization using linear shape functions in the finite element method is proposed to improve the method convergence. This initialization only takes a small percentage of the total computational time. The proposed eigenvalue solver is compared to the standard power iteration method, the Krylov-Schur method and the generalized Davidson method. The numerical results show that it reduces the computational time to solve the eigenvalue problem.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2019.1602768