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 | # Authors:
# Loic Gouarin <loic.gouarin@cmap.polytechnique.fr>
# Nicole Spillane <nicole.spillane@cmap.polytechnique.fr>
#
# License: BSD 3 clause
from __future__ import print_function, division
import sys, petsc4py
petsc4py.init(sys.argv)
import mpi4py.MPI as mpi
from petsc4py import PETSc
import numpy as np
from GenEO import *
def rhs(coords, rhs):
n = rhs.shape
rhs[..., 1] = -9.81
OptDB = PETSc.Options()
Lx = OptDB.getInt('Lx', 4)
Ly = OptDB.getInt('Ly', 1)
n = OptDB.getInt('n', 16)
nx = OptDB.getInt('nx', Lx*n)
ny = OptDB.getInt('ny', Ly*n)
E1 = OptDB.getReal('E1', 10**12)
E2 = OptDB.getReal('E2', 10**6)
nu1 = OptDB.getReal('nu1', 0.4)
nu2 = OptDB.getReal('nu2', 0.4)
test_case = OptDB.getString('test_case', 'default')
isPCNew = OptDB.getBool('PCNew', True)
hx = Lx/(nx - 1)
hy = Ly/(ny - 1)
da = PETSc.DMDA().create([nx, ny], dof=2, stencil_width=1)
da.setUniformCoordinates(xmax=Lx, ymax=Ly)
da.setMatType(PETSc.Mat.Type.IS)
def lame_coeff(x, y, v1, v2):
output = np.empty(x.shape)
mask = np.logical_or(np.logical_and(.2<=y, y<=.4),np.logical_and(.6<=y, y<=.8))
output[mask] = v1
output[np.logical_not(mask)] = v2
return output
# non constant Young's modulus and Poisson's ratio
E = buildCellArrayWithFunction(da, lame_coeff, (E1,E2))
nu = buildCellArrayWithFunction(da, lame_coeff, (nu1,nu2))
lamb = (nu*E)/((1+nu)*(1-2*nu))
mu = .5*E/(1+nu)
class callback:
def __init__(self, da):
self.da = da
ranges = da.getRanges()
ghost_ranges = da.getGhostRanges()
self.slices = []
for r, gr in zip(ranges, ghost_ranges):
self.slices.append(slice(gr[0], r[1]))
self.slices = tuple(self.slices)
self.it = 0
def __call__(self, locals):
pyKSP = locals['self']
proj = pyKSP.mpc.proj
if self.it == 0:
work, _ = proj.A.getVecs()
for i, vec in enumerate(proj.V0):
if vec:
proj.works = vec.copy()
else:
proj.works.set(0.)
work.set(0)
proj.scatter_l2g(proj.works, work, PETSc.InsertMode.ADD_VALUES)
viewer = PETSc.Viewer().createVTK('output.d/coarse_vec_{}.vts'.format(i), 'w', comm = PETSc.COMM_WORLD)
tmp = self.da.createGlobalVec()
tmpl_a = self.da.getVecArray(tmp)
work_a = self.da.getVecArray(work)
tmpl_a[:] = work_a[:]
tmp.view(viewer)
viewer.destroy()
self.it += 1
x = da.createGlobalVec()
b = buildRHS(da, [hx, hy], rhs)
A = buildElasticityMatrix(da, [hx, hy], lamb, mu)
A.assemble()
bcApplyWest(da, A, b)
#Setup the preconditioner (or multipreconditioner) and the coarse space
pcbnn = PCNew(A)
Apos = pcbnn.Apos
############compute x FOR INITIALIZATION OF PCG
# Random initial guess
print('Random rhs')
b.setRandom()
#Pre-compute solution in coarse space
#Required for PPCG (projected preconditioner)
#Doesn't hurt or help the hybrid and additive preconditioners
#the initial guess is passed to the PCG below with the option ksp.setInitialGuessNonzero(True)
if mpi.COMM_WORLD.rank == 0:
print('solve a problem for Apos preconditioned by H2')
############END of: compute x FOR INITIALIZATION OF PCG
#############SETUP KSP
ksp_Apos = pcbnn.ksp_Apos
# ksp_Apos.setOptionsPrefix("")
# pc_Apos = ksp_Apos.pc
# pc_Apos = pcbnn.pc_Apos
# pc_Apos.setFromOptions()
# ksp_Apos.setType("cg")
#ksp_Apos.setComputeEigenvalues(True)
# #pyKSP.callback = callback(da)
# ksp_Apos.setType(ksp_Apos.Type.PYTHON)
# pyKSP = KSP_PCG()
# ksp_Apos.setPythonContext(pyKSP)
# ksp_Apos.setFromOptions()
#### END SETUP KSP
###### SOLVE:
ksp_Apos.solve(b, x)
Aposx = x.duplicate()
pcbnn.Apos.mult(x,Aposx)
print(f'norm of Apos x - b = {(Aposx - b).norm()}, norm of b = {b.norm()}')
|