Minimal residual method applied to the transport equation

During the last years, various algorithms solving the transport equation in slab geometry have been proposed in the literature [2–4,6,7]. Most of them use a convergence acceleration based on a Picard type algorithm called the source iteration method [4,7]. New non-accelerated algorithms have been recently introduced [1,2]. We develop here a non-accelerated method based on two points: a splitting of the collision operator and an infinite dimensional adaptation of the minimal residual method. We first prove the theoretical convergence of the method in the frame of non-reflecting boundary conditions. Then we compare numerically this method with existing non accelerated schemes. It gives good results which could even be further improved by adding a DSA kind acceleration.