240 research outputs found
BootCMatch: A software package for bootstrap AMG based on graph weighted matching
This article has two main objectives: one is to describe some extensions of an adaptive Algebraic Multigrid (AMG) method of the form previously proposed by the first and third authors, and a second one is to present a new software framework, named BootCMatch, which implements all the components needed to build and apply the described adaptive AMG both as a stand-alone solver and as a preconditioner in a Krylov method. The adaptive AMG presented is meant to handle general symmetric and positive definite (SPD) sparse linear systems, without assuming any a priori information of the problem and its origin; the goal of adaptivity is to achieve a method with a prescribed convergence rate. The presented method exploits a general coarsening process based on aggregation of unknowns, obtained by a maximum weight matching in the adjacency graph of the system matrix. More specifically, a maximum product matching is employed to define an effective smoother subspace (complementary to the coarse space), a process referred to as compatible relaxation, at every level of the recursive two-level hierarchical AMG process.
Results on a large variety of test cases and comparisons with related work demonstrate the reliability and efficiency of the method and of the software
Multi-GPU aggregation-based AMG preconditioner for iterative linear solvers
We present and release in open source format a sparse linear solver which
efficiently exploits heterogeneous parallel computers. The solver can be easily
integrated into scientific applications that need to solve large and sparse
linear systems on modern parallel computers made of hybrid nodes hosting NVIDIA
Graphics Processing Unit (GPU) accelerators.
The work extends our previous efforts in the exploitation of a single GPU
accelerator and proposes an implementation, based on the hybrid MPI-CUDA
software environment, of a Krylov-type linear solver relying on an efficient
Algebraic MultiGrid (AMG) preconditioner already available in the BootCMatchG
library. Our design for the hybrid implementation has been driven by the best
practices for minimizing data communication overhead when multiple GPUs are
employed, yet preserving the efficiency of the single GPU kernels. Strong and
weak scalability results on well-known benchmark test cases of the new version
of the library are discussed. Comparisons with the Nvidia AmgX solution show an
improvement of up to 2.0x in the solve phase
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