Coarse Mesh Rebalance Acceleration Applied to an Iterative Domain Decomposition Method on Unstructured Mesh

International audienceAn iterative domain decomposition method (DDM) is implemented inside the APOLLO3 Sntransport core solver MINARET. Based on a block-Jacobi algorithm, the method inherently suffers a convergencepenalty in terms of both computing time and number of iterations. An acceleration method has to bedeveloped in order to overcome this difficulty. This paper investigates a nonlinear coarse mesh rebalance (CMR)method that favors the way information propagates through the core when domain decomposition is used. Thefundamental idea involves updating each subdomain boundary condition thanks to a core-sized low-ordercalculation on a coarse spatial mesh. The numerical convergence is sped up. Performances are meeting theexpectations since the CMR acceleration systematically succeeds in overbalancing the domain decompositionadditional cost. The aim of such a DDM + CMR algorithm is eventually to introduce more parallelism whensolving the spatial transport equation. Nevertheless, parallel computing is not addressed in this paper

A domain decomposition method in APOLLO3R^R solver, MINARET

International audienceThe aim of this paper is to present the last developments made on Domain Decomposition Methodinside the APOLLO3$^R$ core solver, MINARET. The fundamental idea consists in splitting a large boundaryvalue problem into several similar but smaller ones. Since each sub-problem can be solved independently,the Domain Decomposition Method is a natural candidate to introduce more parallel computing intodeterministic schemes. Yet, the real originality of this work does not rest on the well-tried DomainDecomposition Method, but in its implementation inside MINARET. The first validation elements show aperfect equivalence between the reference and the Domain Decomposition schemes, in terms of both$k_{eff}$ and flux mapping. These first results are obtained without any parallelization or acceleration.Nevertheless, the “relatively“ low increase of computation time due to Domain Decomposition is veryencouraging for future performances. So much that one can hope to greatly increase the precisionwithout any major time impact for users. At last, the unstructured space meshing used in MINARET willeventually be improved by adding an optional non conformal map between subdomains. This associationwill make of the new scheme an efficient tool, able to deal with the large variety of geometries offered bynuclear core concepts

Performance study of a parallel domain decomposition method

International audienceThis paper studies the influence of various parameters, in order to improve the performances of a parallel Domain Decomposition Method ($aka$ DDM). If introducing more parallelism represents an opportunity to heighten the performance of deterministic schemes, substantial modifications of their architecture are required. In this context, DDM has been implemented into the Apollo3 multigroup $S_n$ solver, Minaret. The fundamental idea involves splitting a large boundary value problem into several $independent$ subproblems, that can be computed in parallel.Two $DDM$ algorithms are considered. The first one solves a one-group problem per subdomain. The second one is a multigroup block-Jacobi algorithm. To improve performances of these DDM,various parallelism strategies are implemented and compared, depending on the internal structure of the DDM algorithm, the technology chosen (MPI or OpenMP), and the variable parallelized (angular direction or subdomain). Based on these considerations, an efficient $hybrid$ parallelism,suitable for $HPC$ is built a parallel multigroup Jacobi iteration algorithm, using a two layerMPI/OpenMP architecture, gives the best performances for the reactor configuration studied