Paper Info
Title
A Matrix-Free Eigenvalue Solver For The Multigroup Neutron Diffusion Equation
Abstract
The stationary neutron transport equation describes the neutron population and thus, the generated heat, inside a nuclear reactor core. Obtaining the solution of this equation requires to solve a generalized eigenvalue problem efficiently. The majority of the eigenvalue solvers use the factorization of the system matrices to construct preconditioners, such as the ILU decomposition or the ICC decomposition, to speed up the convergence of the methods. The storage of the involved matrices and incomplete factorization demands high quantities of computational memory although a the sparse format is used. This makes the computational memory the limiting factor for this kind of calculations in some personal computers. In this work, we propose a matrix-free preconditioned eigenvalue solver that does not need to have the matrices allocated in memory explicitly. This method is based on the block inverse-free preconditioned Arnoldi method (BIFPAM) with the innovation that uses a preconditioner that is applied from matrix-vector operations. As well as reducing enormously the computational memory, this methodology removes the time to assembly the sparse matrices involved in the system. A two-dimensional and three-dimensional benchmarks are used to study the performance of the methodology proposed.
Year
DOI
Venue
2019
10.1007/978-3-030-22750-0_68
COMPUTATIONAL SCIENCE - ICCS 2019, PT V
Keywords
Field
DocType
Neutron diffusion, Eigenvalue problem, Lambda modes, Matrix free, Block method
Applied mathematics,Neutron transport,Population,Mathematical optimization,Preconditioner,Matrix (mathematics),Computer science,Eigendecomposition of a matrix,Solver,Sparse matrix,Eigenvalues and eigenvectors
Conference
Volume
ISSN
Citations 
11540
0302-9743
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Amanda Carreño100.34
Antoni Vidal-Ferràndiz200.34
Damián Ginestar372.30
G. Verdú4107.93