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

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.