PyMGRIT is a package for the Multigrid-Reduction-in-Time (MGRIT) algorithm in Python.
PyMGRIT is currently developed by Jens Hahne and Stephanie Friedhoff.
The MGRIT algorithm is a reduction-based time-multigrid method for solving time-dependent problems. In contrast to solving sequentially for one time step after the other, the MGRIT algorithm is an iterative method that allows calculating multiple time steps simultaneously by using a time-grid hierarchy. The MGRIT method is a non-intrusive approach that essentially uses the same time integrator as a traditional time-stepping algorithm. Therefore, it is particularly well suited for introducing time parallelism in simulations using existing application codes.
PyMGRIT features:
- Classical Multigrid-Reduction-in-Time (MGRIT) for solving evolutionary systems of equations
- Non-intrusive approach
- Optimal time-multigrid algorithm
- A variety of cycling strategies, relaxation schemes, and coarsening strategies
- Time parallelism
- Specific to space-time problems
- Space & time parallelism
- Additional coarsening in space
@MISC{PyMGRIT,
author = "Hahne, J. and Friedhoff, S.",
title = "{PyMGRIT}: Multigrid-Reduction-in-Time in {Python} v1.0",
year = "2020",
url = "https://github.com/pymgrit/pymgrit",
note = "Release 1.0"
}
PyMGRIT requires mpicc
(from openmpi
or mpich
)
>>> pip3 install pymgrit
or
>>> git clone https://github.com/pymgrit/pymgrit.git >>> cd pymgrit >>> pip3 install .
PyMGRIT is easy to use! The following code generates a discrete Dahlquist test problem and solves the resulting linear system using a two-level MGRIT algorithm.:
# Import PyMGRIT
from pymgrit import *
# Create Dahlquist's test problem with 101 time steps in the interval [0, 5]
dahlquist = Dahlquist(t_start=0, t_stop=5, nt=101)
# Construct a two-level multigrid hierarchy for the test problem using a coarsening factor of 2
dahlquist_multilevel_structure = simple_setup_problem(problem=dahlquist, level=2, coarsening=2)
# Set up the MGRIT solver for the test problem and set the solver tolerance to 1e-10
mgrit = Mgrit(problem=dahlquist_multilevel_structure, tol=1e-10)
# Solve the test problem
info = mgrit.solve()
Program output:
INFO - 21-02-20 16:18:43 - Start setup
INFO - 21-02-20 16:18:43 - Setup took 0.009232759475708008 s
INFO - 21-02-20 16:18:43 - Start solve
INFO - 21-02-20 16:18:43 - iter 1 | conv: 7.186185937031941e-05 | conv factor: - | runtime: 0.013237237930297852 s
INFO - 21-02-20 16:18:43 - iter 2 | conv: 1.2461067076355103e-06 | conv factor: 0.017340307063501627 | runtime: 0.010195493698120117 s
INFO - 21-02-20 16:18:43 - iter 3 | conv: 2.1015566145245807e-08 | conv factor: 0.016864981158092696 | runtime: 0.008922338485717773 s
INFO - 21-02-20 16:18:43 - iter 4 | conv: 3.144127445017594e-10 | conv factor: 0.014960945726074891 | runtime: 0.0062139034271240234 s
INFO - 21-02-20 16:18:43 - iter 5 | conv: 3.975214076032893e-12 | conv factor: 0.01264329816633959 | runtime: 0.006150722503662109 s
INFO - 21-02-20 16:18:43 - Solve took 0.05394101142883301 s
INFO - 21-02-20 16:18:43 - Run parameter overview
time interval : [0.0, 5.0]
number of time points : 101
max dt : 0.05000000000000071
number of levels : 2
coarsening factors : [2]
cf_iter : 1
nested iteration : True
cycle type : V
stopping tolerance : 1e-10
time communicator size : 1
space communicator size : 1
For documentation see https://pymgrit.github.io/pymgrit/
Create an issue.
Look at the Quickstart, Tutorial or the Examples.