/
B_multistep_SDC.py
170 lines (140 loc) · 6.09 KB
/
B_multistep_SDC.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
import os
from pathlib import Path
from pySDC.helpers.stats_helper import get_sorted
from pySDC.helpers.visualization_tools import show_residual_across_simulation
from pySDC.implementations.controller_classes.controller_nonMPI import controller_nonMPI
from pySDC.implementations.problem_classes.HeatEquation_ND_FD import heatNd_unforced
from pySDC.implementations.sweeper_classes.generic_implicit import generic_implicit
from pySDC.implementations.transfer_classes.TransferMesh import mesh_to_mesh
def main():
"""
A simple test program to do compare PFASST with multi-step SDC
"""
# initialize level parameters
level_params = dict()
level_params['restol'] = 5e-10
level_params['dt'] = 0.125
# initialize sweeper parameters
sweeper_params = dict()
sweeper_params['quad_type'] = 'RADAU-RIGHT'
sweeper_params['num_nodes'] = [3]
sweeper_params['QI'] = 'LU'
# initialize problem parameters
problem_params = dict()
problem_params['nu'] = 0.1 # diffusion coefficient
problem_params['freq'] = 2 # frequency for the test value
problem_params['bc'] = 'dirichlet-zero' # boundary conditions
# initialize step parameters
step_params = dict()
step_params['maxiter'] = 50
# initialize space transfer parameters
space_transfer_params = dict()
space_transfer_params['rorder'] = 2
space_transfer_params['iorder'] = 6
# initialize controller parameters
controller_params = dict()
controller_params['logger_level'] = 40
# fill description dictionary for easy step instantiation
description = dict()
description['problem_class'] = heatNd_unforced
description['sweeper_class'] = generic_implicit
description['sweeper_params'] = sweeper_params
description['level_params'] = level_params
description['step_params'] = step_params
description['space_transfer_class'] = mesh_to_mesh
description['space_transfer_params'] = space_transfer_params
# set up parameters for PFASST run
problem_params['nvars'] = [63, 31]
description['problem_params'] = problem_params.copy()
description_pfasst = description.copy()
# set up parameters for MSSDC run
problem_params['nvars'] = [63]
description['problem_params'] = problem_params.copy()
description_mssdc = description.copy()
controller_params['mssdc_jac'] = True
controller_params_jac = controller_params.copy()
controller_params['mssdc_jac'] = False
controller_params_gs = controller_params.copy()
# set time parameters
t0 = 0.0
Tend = 1.0
# set up list of parallel time-steps to run PFASST/MSSDC with
num_proc = 8
# instantiate controllers
controller_mssdc_jac = controller_nonMPI(
num_procs=num_proc, controller_params=controller_params_jac, description=description_mssdc
)
controller_mssdc_gs = controller_nonMPI(
num_procs=num_proc, controller_params=controller_params_gs, description=description_mssdc
)
controller_pfasst = controller_nonMPI(
num_procs=num_proc, controller_params=controller_params, description=description_pfasst
)
# get initial values on finest level
P = controller_mssdc_jac.MS[0].levels[0].prob
uinit = P.u_exact(t0)
# call main functions to get things done...
uend_pfasst, stats_pfasst = controller_pfasst.run(u0=uinit, t0=t0, Tend=Tend)
uend_mssdc_jac, stats_mssdc_jac = controller_mssdc_jac.run(u0=uinit, t0=t0, Tend=Tend)
uend_mssdc_gs, stats_mssdc_gs = controller_mssdc_gs.run(u0=uinit, t0=t0, Tend=Tend)
# compute exact solution and compare for both runs
uex = P.u_exact(Tend)
err_mssdc_jac = abs(uex - uend_mssdc_jac)
err_mssdc_gs = abs(uex - uend_mssdc_gs)
err_pfasst = abs(uex - uend_pfasst)
diff_jac = abs(uend_mssdc_jac - uend_pfasst)
diff_gs = abs(uend_mssdc_gs - uend_pfasst)
diff_jac_gs = abs(uend_mssdc_gs - uend_mssdc_jac)
Path("data").mkdir(parents=True, exist_ok=True)
f = open('data/step_8_B_out.txt', 'w')
out = 'Error PFASST: %12.8e' % err_pfasst
f.write(out + '\n')
print(out)
out = 'Error parallel MSSDC: %12.8e' % err_mssdc_jac
f.write(out + '\n')
print(out)
out = 'Error serial MSSDC: %12.8e' % err_mssdc_gs
f.write(out + '\n')
print(out)
out = 'Diff PFASST vs. parallel MSSDC: %12.8e' % diff_jac
f.write(out + '\n')
print(out)
out = 'Diff PFASST vs. serial MSSDC: %12.8e' % diff_gs
f.write(out + '\n')
print(out)
out = 'Diff parallel vs. serial MSSDC: %12.8e' % diff_jac_gs
f.write(out + '\n')
print(out)
# convert filtered statistics to list of iterations count, sorted by process
iter_counts_pfasst = get_sorted(stats_pfasst, type='niter', sortby='time')
iter_counts_mssdc_jac = get_sorted(stats_mssdc_jac, type='niter', sortby='time')
iter_counts_mssdc_gs = get_sorted(stats_mssdc_gs, type='niter', sortby='time')
# compute and print statistics
for item_pfasst, item_mssdc_jac, item_mssdc_gs in zip(
iter_counts_pfasst, iter_counts_mssdc_jac, iter_counts_mssdc_gs
):
out = 'Number of iterations for time %4.2f (PFASST/parMSSDC/serMSSDC): %2i / %2i / %2i' % (
item_pfasst[0],
item_pfasst[1],
item_mssdc_jac[1],
item_mssdc_gs[1],
)
f.write(out + '\n')
print(out)
f.close()
# call helper routine to produce residual plot
show_residual_across_simulation(stats_mssdc_jac, 'data/step_8_residuals_mssdc_jac.png')
show_residual_across_simulation(stats_mssdc_gs, 'data/step_8_residuals_mssdc_gs.png')
assert os.path.isfile('data/step_8_residuals_mssdc_jac.png')
assert os.path.isfile('data/step_8_residuals_mssdc_gs.png')
assert diff_jac < 3.1e-10, (
"ERROR: difference between PFASST and parallel MSSDC controller is too large, got %s" % diff_jac
)
assert diff_gs < 3.1e-10, (
"ERROR: difference between PFASST and serial MSSDC controller is too large, got %s" % diff_gs
)
assert diff_jac_gs < 3.1e-10, (
"ERROR: difference between parallel and serial MSSDC controller is too large, got %s" % diff_jac_gs
)
if __name__ == "__main__":
main()