3D Cartesian Transport Sweep for Massively Parallel Architectures with PaRSEC

Abstract

High-fidelity nuclear power plant core simulations require solving the Boltzmann transport equation. In discrete ordinates methods, the most computationally demanding operation of this equation is the sweep operation. Considering the evolution of computer architectures, we propose in this paper, as a first step toward heterogeneous distributed architectures, a hybrid parallel implementation of the sweep operation on top of the generic task-based runtime system: PARSEC. Such an implementation targets three nested levels of parallelism: message passing, multi-threading, and vectorization. A theoretical performance model was designed to validate the approach and help the tuning of the multiple parameters involved in such an approach. The proposed parallel implementation of the Sweep achieves a sustained performance of 6.1 Tflop/s, corresponding to 33.9% of the peak performance of the targeted supercomputer. This implementation compares favorably with state-ofart solvers such as PARTISN; and it can therefore serve as a building block for a massively parallel version of the neutron transport solver DOMINO developed at EDF.

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

“…The paper is organized as follows. In Section 2, we describe the equations to be solved, the different discretization schemes, the main algorithm and the three nested levels of parallelism used in the sweep implementation described in [1]. In Section 3, the PDSA algorithm and its implementation are described and some details are given regarding the correct coupling between the Transport DD0 discretization and the Finite Element method used in the PDSA.…”

“…Hence, the cell (0, 0) located at the bottom-left corner is the first to be processed. The treatment of this cell allows for the updating of outgoing fluxes ψ R and ψ T , that satisfy the dependencies of cells (0, 1) and (1,0). These dependencies on the processing of cells define a sequential nature throughout the progression of the sweep operation: two adjacent cells belonging to successive diagonals cannot be processed simultaneously.…”

High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation

“…Because of the upwind structure of the numerical flux, it appears that the transport matrix is often block-triangular. This is very interesting because this allows to applying implicit schemes to (41) without the costly inversion of linear systems [32]. We can provide the formal structure of L h through the construction of a directed graph G with a set of vertices V and a set of edges E ⊂ V × V. The vertices of the graph are associated to the (real or fictitious) cells of M. Now consider two cells L and R with a common face F LR .…”

Task-Based Parallelization of an Implicit Kinetic Scheme

“…Because of the upwind structure of the numerical flux, it appears that the transport matrix is often block-triangular. This is very interesting because this allows to apply implicit schemes to (3.9) without the costly inversion of linear systems [11]. We can provide the formal structure of L h through the construction of a directed graph G with a set of vertices V and a set of edges E ⊂ V × V. The vertices of the graph are associated to the (real or fictitious) cells of M. Consider now two cells L and R with a common face F LR .…”