Subdomain Deflation Combined with Local AMG: a Case Study Using AMGCL Library
For computational scientists solving large sparse linear systems, this work offers a practical, scalable preconditioner that reduces communication overhead, but the improvements are incremental over existing methods.
The paper proposes a scalable distributed memory preconditioner combining subdomain deflation and local algebraic multigrid, implemented in the open-source AMGCL library. It demonstrates improved weak and strong scalability over traditional global AMG (Trilinos ML) for Poisson-like and Navier-Stokes problems on CPU and CPU/GPU systems.
The paper proposes a combination of the subdomain deflation method and local algebraic multigrid as a scalable distributed memory preconditioner that is able to solve large linear systems of equations. The implementation of the algorithm is made available for the community as part of an open source AMGCL library. The solution targets both homogeneous (CPU-only) and heterogeneous (CPU/GPU) systems, employing hybrid MPI/OpenMP approach in the former and a combination of MPI, OpenMP, and CUDA in the latter cases. The use of OpenMP minimizes the number of MPI processes, thus reducing the communication overhead of the deflation method and improving both weak and strong scalability of the preconditioner. The examples of scalar, Poisson-like, systems as well as non-scalar problems, stemming out of the discretization of the Navier-Stokes equations, are considered in order to estimate performance of the implemented algorithm. A comparison with a traditional global AMG preconditioner based on a well-established Trilinos ML package is provided.