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

Efficient parallel solution of the 3D stationary Boltzmann transport equation for diffusive problems

“…• A novel scalable PDSA acceleration technique for diffusive problem introduced in [2] and applied for the first time to 3D transport computations. This method is easy to implement provided a fast single-domain sharedmemory diffusion solver.…”

“…On the other hand, if the diffusion solver is parallelized, as presented in [7,8] using a domain decomposition method, the iteration count to the solution increases with the number of subdomains, and can lead to a poor global scalability [19]. To remedy this issue, a variant of the DSA scheme has been recently proposed by F. Févotte in [2].…”

“…The general presentation and the convergence proof of the Piecewise Diffusion Synthetic Acceleration (PDSA) method are given in [2]. We recall that the purpose of this method is similar to that of DSA: evaluate an approximation, ˜ k+ 1 2 , of the error on the scalar flux, ¯ k+ 1 2 , to be used for correcting the scalar flux, φ k+ 1 2 .…”

“…As shown in [2], for sufficiently diffusive and optically thick problems, the PDSA solution ˜ D is an approximation of the global DSA solution ˜ . The accelerated S N flux is thus finally given by:…”

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This paper presents an efficient parallel method for the deterministic solution of the 3D stationary Boltzmann transport equation applied to diffusive problems such as nuclear core criticality computations. Based on standard MultiGroup-Sn-DD discretization schemes, our approach combines a highly efficient nested parallelization strategy [1] with the PDSA parallel acceleration technique [2] applied for the first time to 3D transport problems. These two key ingredients enable us to solve extremely large neutronic problems involving up to 10 12 degrees of freedom in less than an hour using 64 super-computer nodes.

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