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Generalized Minimal Residual Algorithm and Polynomial Preconditioning Solver for 2-D Boltzmann Transport Equation

Abdelkader TIZAOUI

Abstract


A polynomial preconditioning technique is proposed to accelerate the Generalized Minimal Residual algorithm in this paper for solving the neutron transport equation in two geometry. This preconditioning is based on a splitting of the collision operator and an infinite dimensional adaptation of a polynomial preconditioning. The aim of this paper is to analyze a theoretical and numerical aspects of the Generalized Minimal Residual algorithm algorithm after using a polynomial preconditioning. One of the advantages of this algorithm is that it gives a good rate of convergence, but it does not need any extra parameter calculation. Some numerical experiments based on the Generalized Minimal Residual algorithm are discussed and compared with existing schemes.

Keywords


Neutron transport equation, integro-differentials operators, splitting, Generalized Minimal Residual algorithm, preconditioning.

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