Open Access Open Access  Restricted Access Subscription or Fee Access

Incomplete factorization preconditioning and GMRES algorithm applied to the 1-D neutron transport equation

Abdelkader Tizaoui


In this work we proposed to solve the neutron transport equation in slab geometry by a infinite dimensional adaptation of GMRES algorithm accelerated by the incomplete factorization preconditioning technique. This preconditioning is based on a splitting of the collision operator taking account the characteristics of the transport operator. The theoretical and numerical aspects of this algorithm in the frame of non-reflexing boundary conditions are
given here. One of the advantage of this algorithm is that it gives a good rate of convergence, but it does not need any extra parameter calculation. Some numerical experiments of this algorithm are discussed and compared with existing schemes are given at the end of this work.


Neutron transport equation, integro-differentials operators, splitting, GMRES algorithm, preconditioning.

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.