Schwarz type preconditioners for the neutron diffusion equation
Journal article, 2017

Domain decomposition is a mature methodology that has been used to accelerate the convergence of partial differential equations. Even if it was devised as a solver by itself, it is usually employed together with Krylov iterative methods improving its rate of convergence, and providing scalability with respect to the size of the problem. In this work, a high order finite element discretization of the neutron diffusion equation is considered. In this problem the preconditioning of large and sparse linear systems arising from a source driven formulation becomes necessary due to the complexity of the problem. On the other hand, preconditioners based on an incomplete factorization are very expensive from the point of view of memory requirements. The acceleration of the neutron diffusion equation is thus studied here by using alternative preconditioners based on domain decomposition techniques inside Schur complement methodology. The study considers substructuring preconditioners, which do not involve overlapping, and additive Schwarz preconditioners, where some overlapping between the subdomains is taken into account. The performance of the different approaches is studied numerically using two-dimensional and three-dimensional problems. It is shown that some of the proposed methodologies outperform incomplete LU factorization for preconditioning as long as the linear system to be solved is large enough, as it occurs for three-dimensional problems. They also outperform classical diagonal Jacobi preconditioners, as long as the number of systems to be solved is large enough in such a way that the overhead of building the preconditioner is less than the improvement in the convergence rate.

Finite element method

Schwarz preconditioner


Neutron diffusion


Antoni Vidal

Polytechnic University of Valencia (UPV)

Sebastian Gonzalez-Pintor

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Damian Ginestar

Polytechnic University of Valencia (UPV)

Gumersindo Verdu

Polytechnic University of Valencia (UPV)

Christophe Demaziere

Chalmers, Physics, Subatomic and Plasma Physics

Journal of Computational and Applied Mathematics

0377-0427 (ISSN)

Vol. 309 563-574

Subject Categories

Subatomic Physics

Other Engineering and Technologies

Computational Mathematics

Other Physics Topics

Areas of Advance



Basic sciences



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3/6/2018 1