Fast non-overlapping Schwarz domain decomposition methods for solving the neutron diffusion equation

Studying numerically the steady state of a nuclear core reactor is expensive, in terms of memory storage and computational time. In order to address both requirements, one can use a domain decomposition method, implemented on a parallel computer. We present here such a method for the mixed neutron diffusion equations, discretized with Raviart-Thomas-Nédélec finite elements. This method is based on the Schwarz iterative algorithm with Robin interface conditions to handle communications. We analyse this method from the continuous point of view to the discrete point of view, and we give some numerical results in a realistic highly heterogeneous 3D configuration. Computations are carried out with the MINOS solver of the APOLLO3®. 1APOLLO3 is a registered trademark in France.¹ neutronics code.