Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

PyAMG: Algebraic Multigrid Solvers in Python

Journal Article · · Journal of Open Source Software
DOI:https://doi.org/10.21105/joss.04142· OSTI ID:2433956
 [1];  [2];  [3]
  1. Google Research, Mountain View, CA (United States)
  2. Univ. of Illinois at Urbana-Champaign, IL (United States)
  3. Univ. of New Mexico, Albuquerque, NM (United States)
+ Show Author Affiliations

PyAMG is a Python package of algebraic multigrid (AMG) solvers and supporting tools for approximating the solution to large, sparse linear systems of algebraic equations, Ax = b, where A is an n × n sparse matrix. Sparse linear systems arise in a range of problems in science, from fluid flows to solid mechanics to data analysis. While the direct solvers available in SciPy’s sparse linear algebra package (scipy.sparse.linalg) are highly efficient, in many cases iterative methods are preferred due to overall complexity. However, the iterative methods in SciPy, such as CG and GMRES, often require an efficient preconditioner in order to achieve a lower complexity. Preconditioning is a powerful tool whereby the conditioning of the linear system and convergence rate of the iterative method are both dramatically improved. PyAMG constructs multigrid solvers for use as a preconditioner in this setting. A summary of multigrid and algebraic multigrid solvers can be found in Olson (2015a), in Olson (2015b), and in Falgout (2006); a detailed description can be found in Briggs et al. (2000) and Trottenberg et al. (2001).

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
Grant/Contract Number:
89233218CNA000001
OSTI ID:
2433956
Report Number(s):
LA-UR--23-26551
Journal Information:
Journal of Open Source Software, Journal Name: Journal of Open Source Software Journal Issue: 72 Vol. 7; ISSN 2475-9066
Publisher:
Open Source Initiative - NumFOCUSCopyright Statement
Country of Publication:
United States
Language:
English

References (9)

Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems journal September 1996
BoomerAMG: A parallel algebraic multigrid solver and preconditioner journal April 2002
An introduction to algebraic multigrid journal November 2006
AMGCL: An Efficient, Flexible, and Extensible Algebraic Multigrid Implementation journal May 2019
Adaptive Smoothed Aggregation ($\alpha$SA) Multigrid journal January 2005
A Multigrid Tutorial, Second Edition book January 2000
Exposing Fine-Grained Parallelism in Algebraic Multigrid Methods journal January 2012
AmgX: A Library for GPU Accelerated Algebraic Multigrid and Preconditioned Iterative Methods journal January 2015
A Root-Node--Based Algebraic Multigrid Method journal January 2017

Similar Records

An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems
Conference · Mon Dec 30 23:00:00 EST 1996 · OSTI ID:433348
On performance of Krylov smoothing for fully-coupled AMG preconditioners for VMS resistive MHD
Program Document · Wed Nov 01 00:00:00 EDT 2017 · OSTI ID:1429689
A Comparison of Classical and Aggregation-Based Algebraic Multigrid Preconditioners for High-Fidelity Simulation of Wind Turbine Incompressible Flows
Journal Article · Tue Oct 29 00:00:00 EDT 2019 · SIAM Journal on Scientific Computing · OSTI ID:1577955

Related Subjects

97 MATHEMATICS AND COMPUTING
Krylov
algebraic multigrid
computer science
iterative methods
preconditioning
sparse matrix