Abstract
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.
Highlights
SALVATORE FILIPPONE, Centre for Computational Engineering Sciences, School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, United Kingdom
We always used the Algebraic Multigrid (AMG) method as preconditioner for the Flexible Conjugate Gradient (FCG) Krylov method. We present both results related to the use of a single component AMG, as well as results obtained with the bootstrap process of Section 5 applied to obtain a composite AMG solver with a prescribed convergence rate
We observed that if we apply BootCMatch for building a bootstrap AMG based on a symmetrized multiplicative composition, a composite preconditioner with seven components and an estimated convergence rate of 0.92, with a building cost of 40.88 seconds, we can attain convergence in 1, 928 iterations within 877.58 seconds of solver time
Summary
SALVATORE FILIPPONE, Centre for Computational Engineering Sciences, School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, United Kingdom. VASSILEVSKI, Department of Mathematics and Statistics, Portland State University and Center for Applied Scientific Computing, Lawrence Livermore National Laboratory. 39 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 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. CCS Concepts: Mathematics of computing → Solvers; Additional Key Words and Phrases: Algebraic multigrid, preconditioner, iterative solver, graph matching
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