PyAMG requires numpy
and scipy
pip install pyamg
or
python setup.py install
PyAMG is a library of Algebraic Multigrid (AMG) solvers with a convenient Python interface.
PyAMG is developed by Nathan Bell, Luke Olson, and Jacob Schroder, in the Deparment of Computer Science at the University of Illinois at Urbana-Champaign. Portions of the project were partially supported by the NSF under award DMS-0612448.
@MISC{BeOlSc2011, author = "Bell, W. N. and Olson, L. N. and Schroder, J. B.", title = "{PyAMG}: Algebraic Multigrid Solvers in {Python} v3.0", year = "2015", url = "http://www.pyamg.org", note = "Release 3.0" }
Contact the pyamg-user group
Look at the Tutorial or the Examples (for instance the 0STARTHERE example)
AMG is a multilevel technique for solving large-scale linear systems with optimal or near-optimal efficiency. Unlike geometric multigrid, AMG requires little or no geometric information about the underlying problem and develops a sequence of coarser grids directly from the input matrix. This feature is especially important for problems discretized on unstructured meshes and irregular grids.
PyAMG features implementations of:
- Ruge-Stuben (RS) or Classical AMG
- AMG based on Smoothed Aggregation (SA)
and experimental support for:
- Adaptive Smoothed Aggregation (αSA)
- Compatible Relaxation (CR)
The predominant portion of PyAMG is written in Python with a smaller amount of supporting C++ code for performance critical operations.
PyAMG is easy to use! The following code constructs a two-dimensional Poisson problem and solves the resulting linear system with Classical AMG.
from scipy import *
from scipy.linalg import *
from pyamg import *
from pyamg.gallery import *
A = poisson((500,500), format='csr') # 2D Poisson problem on 500x500 grid
ml = ruge_stuben_solver(A) # construct the multigrid hierarchy
print ml # print hierarchy information
b = rand(A.shape[0]) # pick a random right hand side
x = ml.solve(b, tol=1e-10) # solve Ax=b to a tolerance of 1e-8
print "residual norm is", norm(b - A*x) # compute norm of residual vector
Program output:
multilevel_solver Number of Levels: 6 Operator Complexity: 2.198 Grid Complexity: 1.666 Coarse Solver: 'pinv2' level unknowns nonzeros 0 250000 1248000 [45.50%] 1 125000 1121002 [40.87%] 2 31252 280662 [10.23%] 3 7825 70657 [ 2.58%] 4 1937 17973 [ 0.66%] 5 484 4728 [ 0.17%] residual norm is 1.86112114946e-06