A Domain Decomposition Method Applied to Large Eigenvalue Problems in Neutron Physics

International audienceThe simulation of the neutron transport inside a nuclear reactor leads to the computation of the lowest eigen pair of a simplified transport operator. This computation is done by a power inverse algorithm accelerated by a Chebyshev polynomials based process. At each iteration, a large linear system is solved inexactly by a block Gauss-Seidel algorithm. For our applications, one Gauss-Seidel iteration is already sufficient to ensure the right convergence of the inverse power algorithm. For the approximate resolution of the linear system at each inverse power iteration, we propose a non overlapping domain decomposition based on the introduction of Lagrange multipliers in order to: - get a parallel algorithm, which allows to circumvent memory consumption problem and to reduce the computational time; - deal with different numerical approximations in each subdomain; - minimize the code modifications in our industrial solver. When the Chebyshev acceleration process is switched off, the method performs well on up to 100 processors for an industrial test case. It exhibits a good efficiency which allows us to realize some computations beyond the reach of standard workstations. Besides, we study the efficiency of the Chebyshev acceleration process in our domain decomposition method