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

Abdelkader Tizaoui

Abstract



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.

Keywords


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

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