No abstract

Journal of Computational Physics 222 (2007) 86-109. doi:10.1016/j.jcp.2006.06.049Received by publisher: 2005-10-25Harvest Date: 2016-01-04 12:20:04DOI: 10.1016/j.jcp.2006.06.049Page Range: 86-10

a b s t r a c tA reactivity computation consists of computing the highest eigenvalue of a generalized eigenvalue problem, for which an inverse power algorithm is commonly used. Very fine modelizations are difficult to treat for our sequential solver, based on the simplified transport equations, in terms of memory consumption and computational time.A first implementation of a Lagrangian based domain decomposition method brings to a poor parallel efficiency because of an increase in the power iterations [1]. In order to obtain a high parallel efficiency, we improve the parallelization scheme by changing the location of the loop over the subdomains in the overall algorithm and by benefiting from the characteristics of the Raviart-Thomas finite element. The new parallel algorithm still allows us to locally adapt the numerical scheme (mesh, finite element order). However, it can be significantly optimized for the matching grid case. The good behavior of the new parallelization scheme is demonstrated for the matching grid case on several hundreds of nodes for computations based on a pin-by-pin discretization.

The simulation of the neutron transport inside a nuclear reactor leads to the computation of the lowest eigen pair of a simplified transport operator. Whereas the sequential solution at our disposal today is really efficient, we are not able to run some industrial cases due to the memory consumption and the computational time. This problem brings us to study parallel strategies.In order to re-use an important part of the solver and to bypass some limitations of conforming cartesian meshes, we propose a non overlapping domain decomposition based on the introduction of Lagrange multipliers. The method performs well on up to 100 processors for an industrial test case.