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

• Published in: Journal of computational physics Vol. 230; no. 5; pp. 2004 - 2020
• Main Authors: Barrault, M., Lathuilière, B., Ramet, P., Roman, J.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 01.03.2011; Elsevier
• Subjects: Algorithms; Computation; Computational techniques; Computer Science; Distributed, Parallel, and Cluster Computing; Domain decomposition method; Eigenvalues; Exact sciences and technology; Finite element method; HPC; Matching; Mathematical analysis; Mathematical methods in physics; Mathematical models; Parallel processing; Parallelism; Physics; Raviart–Thomas finite element; Simplified transport equation; Transport equations; Parallelism; HPC; Simplified transport equation; Raviart–Thomas finite element; Domain decomposition method; Transport equation; Lagrangian; Decomposition method; Raviart-Thomas finite element; Parallel algorithms; Calculation methods; Discretization; Eigenvalues; Eigenvalue problem; Calculation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2010.11.047

A 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.