PETSc Numerical Scalability Results of New Coarse Corrections for the Optimized Restricted Additive Schwarz Method (Serge Van Criekingen, IDRIS, CNRS)

25.09.2018 14:00

The PETSc library offers tools for the parallel solution of scientific applications modeled by partial differential equations, and the talk will start with a brief description of its potentialities. Among others, PETSc offers the Restricted Additive Schwarz (RAS) method as a preconditioning tool. We implemented two improvements developped by M. J. Gander et al. to this method, namely a new coarse correction and optimized transmission conditions, leading to a two-level Optimized Restricted Additive Schwarz (ORAS) method. A coarse correction is necessary to ensure the scalability of domain decomposition methods applied to elliptic problems. It relies on a coarse grid on which a reduced-size calculation is performed at each iteration, yielding a 2-level method which permits the global propagation of the iterative corrections throughout the entire domain. The new coarse correction considered here is obtained in 1-D by chosing the coarse grid points to be the extreme grid points of the non-overlapping subdomains, and, in 2-D for a rectangular decomposition, by placing four coarse grid points around the cross points of the decomposition. We implemented this coarse correction using the preconditioner composition tool available in PETSc. As for the optimized transmission conditions, they are well-chosen Robin interface conditions implemented by submatrix modification, with only the diagonal entries of the interface nodes required to be modified. Results on a 2D Laplace test case using up to 16 384 CPU cores will be presented, showing very encouraging results, which appear to be competitive with those obtained using the multigrid HYPRE library as interfaced by PETSc.


salle 623, Séminaire d'analyse numérique

Organisé par

Section de mathématiques


Serge Van Criekingen, IDRIS, CNRS

entrée libre


Catégorie: Séminaire

Mots clés: analyse numérique