Quickstart¶
PyMGRIT is easy to use! In the following, we generate a discrete Dahlquist test problem and solve the resulting linear system using a two-level MGRIT algorithm.
Look at the Application Dahlquist for more information about this test problem.
First, import PyMGRIT:
from pymgrit import *
Create Dahlquist’s test problem for the time interval [0, 5] with 101 equidistant time points (100 time points + 1 time point for the initial time t = 0):
dahlquist = Dahlquist(t_start=0, t_stop=5, nt=101)
Construct a multigrid hierarchy for the test problem dahlquist:
dahlquist_multilevel_structure = simple_setup_problem(problem=dahlquist, level=2, coarsening=2)
This tells PyMGRIT to set up a hierarchy with two temporal grid levels using the test problem dahlquist and a temporal coarsening factor of two, i.e., on the fine grid, the number of time points is 101, and on the coarse grid, 51 (=100/2+1) time points are used.
Set up the MGRIT solver for the test problem using dahlquist_multilevel_structure and set the solver tolerance to 1e-10:
mgrit = Mgrit(problem=dahlquist_multilevel_structure, tol=1e-10)
which gives:
INFO - 21-02-20 16:18:43 - Start setup
INFO - 21-02-20 16:18:43 - Setup took 0.009232759475708008 s
Finally, solve the test problem using the solve() routine of the solver mgrit:
info = mgrit.solve()
producing the output:
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
and returning the residual history, setup time, and solve time in dictionary info with key values conv, time_setup, and time_solve, respectively.
Summary¶
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()