A Parallel Implementation of a Two-Level Overlapping Schwarz Method with Energy-Minimizing Coarse Space Based on Trilinos

Abstract

We describe a new implementation of a two-level overlapping Schwarz preconditioner with energy-minimizing coarse space (GDSW) and show numerical results for an additive and a hybrid additive-multiplicative version. Our parallel implementation makes use of the Trilinos software library and provides a framework for parallel two-level Schwarz methods. We show parallel scalability for two and three dimensional scalar second-order elliptic and linear elasticity problems for several thousands of cores. We also discuss techniques for the parallel construction of coarse spaces which are also of interest for other parallel preconditioners and discretization methods using energy minimizing coarse functions. We finally show an application in monolithic fluid-structure interaction, where significant improvements are achieved compared to a standard algebraic, one-level overlapping Schwarz method.

Reduced dimension GDSW coarse spaces for monolithic Schwarz domain decomposition methods for incompressible fluid flow problems

“…The local overlapping problems are solved in serial mode, whereas the coarse problem is solved in parallel mode. We use the default setting of FROSch to determine the number of MPI ranks for the exact coarse solves (cf, References and ). Furthermore, we use one MPI rank per core and one subdomain per MPI rank.…”

“…In contrast to the preconditioners described in References and , which use Lagrangian coarse spaces, GDSW coarse spaces can be constructed in an algebraic fashion without an additional coarse triangulation. We refer to References and for a detailed description of the parallel implementation of GDSW coarse spaces for elliptic and saddle point problems, respectively.…”

“…In our previous implementation of the two‐level AS preconditioner (Equation ), the levels are computed in a sequential way (cf, References , ). However, as the coarse problem is typically solved on a small subset of MPI ranks, most of the cores are idle in the meantime.…”

“…The parallel implementation employed in our numerical simulations is based on our parallel implementation of monolithic two‐level preconditioners described in References , and . The implementation is available in the FROSch framework as a part of the ShyLU package in Trilinos.…”

Steps Towards More Realistic FSI Simulations of Coronary Arteries

“…[2], appropriate space and time discretizations and efficient parallel solution methods, cf. [3], enable the computation of transmural stresses. A benchmark problem shows that the approach is viable and efficient, see [1].…”