Efficient parallel resolution of the simplified transport equations in mixed-dual formulation

Abstract

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.

A fully coupled two‐level Schwarz preconditioner based on smoothed aggregation for the transient multigroup neutron diffusion equations

“…Domain decomposition methods have been receiving increased attention in the nuclear engineering community due to their ability to solve large systems of equations in parallel. In the work of Barrault et al, a nonoverlapping domain decomposition method based on Lagrange multipliers is applied to the simplified transport equations. In the work of Jamelot et al, a nonoverlapping Schwarz method is studied for the one‐speed neutron diffusion equation, and the Robin interface condition is used to exchange data across subdomains.…”

Piecewise Diffusion Synthetic Acceleration scheme for neutron transport simulations in optically thick systems

“…However, industry-grade neutron diffusion solvers are generally sequential, and the elliptic nature of the diffusion equation makes their parallelization a challenging task. Although efficient parallel diffusion solvers can be implemented [7,8], the induced code complexity is often considered a heavy price to pay. The same is also true in the case of alternate acceleration methods such as Coarse-Mesh Finite Differences [9], which are also elliptic in nature and thus difficult to parallelize.…”

Domain decomposition methods for the diffusion equation with low-regularity solution

“…[1,2,3,4], and also for Fick's law and the neutron diffusion equation, see e.g. [5,6,7]. In order to handle non-matching discretizations at the interface of the subdomains, a Lagrange multiplier can be introduced.…”