Choosing the Subregions in Three-Level FROSch Preconditioners

Abstract

Different graph partitioning methods, i.e., linear partioning, parallel hypergraph (PHG) partioning, and two approaches using ParMETIS, are considered to generate an unstructured decomposition of the second-level coarse operator of three-level FROSch (Fast and Robust Overlapping Schwarz) preconditioners in the Trilinos software library. In our context, the parallel hypergraph method shows the most consistent results.

A Three-Level Extension for Fast and Robust Overlapping Schwarz (FROSch) Preconditioners with Reduced Dimensional Coarse Space

“…This also has the nice side effect that the size of the coarse matrix is always the number of interface components times the dimension of the null space. The coarse level is decomposed into subregions in an unstructured way using the Parallel Hypergraph and Graph Partitioning (PGH) from the Trilinos package Zoltan2 [20]; see also [12]. As a Krylov iteration method, we apply the preconditioned conjugate gradient method (PCG) provided by the Trilinos package Belos (BelosPseudoBlockCG).…”

A Multilevel Extension of the GDSW Overlapping Schwarz Preconditioner in Two Dimensions

“…In [18,19], three-level GDSW/RGDSW preconditioners have been introduced for two-and three-dimensional problems and first results have been presented. Furthermore, in [21], the partitioning of the coarse problem has been discussed. In [22], we discuss the three-level implementation in FROSch in detail and show parallel results for scalability up to 220 000 cores on the ALCF Theta supercomputer and 85 000 cores of the SuperMUC-NG supercomputer.…”