A block Arnoldi method for the SPN equations. Issue 1 (1st February 2020)

• Record Type: Journal Article
• Authors: Vidal-Ferràndiz, A.; Carreño, A.; Ginestar, D.; Verdú, G.
• Is Part Of: International journal of computer mathematics. Volume 97:Issue 1/2(2020)
• Page Start: 341
• Page End: 357
• Publication Date: 2020-02-01
• Subjects: Generalized eigenvalue problem -- neutron transport -- multilevel method -- block inverse-free preconditioned Arnoldi method -- generalized Davidson method; 65N30 -- 65N25 -- 35J47; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2019.1602768
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: 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.