Preconditioning the solution of the time-dependent neutron diffusion equation by recycling Krylov subspaces

Abstract

Spectral preconditioners are based on the fact that the convergence rate of the Krylov subspace methods is improved if the eigenvalues of the smallest magnitude of the system matrix are ‘removed’. In this paper, two preconditioning strategies are studied to solve a set of linear systems associated with the numerical integration of the time-dependent neutron diffusion equation. Both strategies can be implemented using the matrix–vector product as the main operation and succeed at reducing the total number of iterations needed to solve the set of systems.

Keywords:

• iterative methods
• matrix-free preconditioners
• Krylov subspace recycling
• neutron diffusion equation
• time integration

2010 AMS Subject Classifications:

• 82D75
• 65F08

Acknowledgement

This work has been partially supported by the Spanish Ministerio de Educación y Ciencia under projects MTM2010-18674 and ENE2011-22823.