def plotmesh3d02():
meshfile = gmsh.buildmesh3d('cylinderkey', 5)
Th = siMesh(meshfile)
plt.close('all')
plt.ion()
DisplayFigures(nfig=4)
plt.figure(1)
siplt.plotmesh(Th, legend=True)
#siplt.plotmesh(Th,d=1,color='black',linewidth=3)
set_axes_equal()
plt.figure(2)
siplt.plotmesh(Th, d=2, legend=True)
plt.axis('off')
set_axes_equal()
plt.figure(3)
siplt.plotmesh(Th,
d=2,
labels=[1, 1000, 1020, 1021],
color='LightGray',
alpha=0.05)
siplt.plotmesh(Th,
d=2,
labels=[10, 11, 31, 2000, 2020, 2021],
legend=True,
alpha=1)
plt.axis('off')
set_axes_equal()
plt.figure(4)
siplt.plotmesh(Th, d=2, color='LightGray', alpha=0.05)
siplt.plotmesh(Th, d=1, legend=True, linewidth=3)
plt.axis('off')
set_axes_equal()
return Th
def find3D01():
meshfile = gmsh.buildmesh3d('cylinder3dom', 15)
Th = siMesh(meshfile)
print('*** 1: print mesh')
print(Th)
d = 3
print('*** 2: print labels of the %d-simplex elementary meshes' % d)
idx = Th.find(d)
print('d=%d, labels=' % d + str(Th.sThlab[idx]))
d = 2
print('*** 3: print labels of the %d-simplex elementary meshes' % d)
idx = Th.find(d)
print('d=%d, labels=' % d + str(Th.sThlab[idx]))
d = 1
print('*** 4: print labels of the %d-simplex elementary meshes' % d)
idx = Th.find(d)
print('d=%d, labels=' % d + str(Th.sThlab[idx]))
d = 3
lab = 10
print('*** 5: print %d-simplex elementary meshes with label %d' % (d, lab))
idx = Th.find(d, labels=lab)
print('Th.sThlab[%d]=%s' % (idx, Th.sThlab[idx]))
print('Th.sTh[%d] is the ' % idx + str(Th.sTh[idx]))
d = 2
lab = 112
print('*** 6: print %d-simplex elementary meshes with label %d' % (d, lab))
idx = Th.find(d, labels=lab)
print('Th.sThlab[%d]=%s' % (idx, Th.sThlab[idx]))
print('Th.sTh[%d] is the ' % idx + str(Th.sTh[idx]))
d = 1
lab = 120
print('*** 7: print %d-simplex elementary meshes with label %d' % (d, lab))
idx = Th.find(d, labels=lab)
print('Th.sThlab[%d]=%s' % (idx, Th.sThlab[idx]))
print('Th.sTh[%d] is the ' % idx + str(Th.sTh[idx]))
def plotmesh3d01():
meshfile = gmsh.buildmesh3d('cylinder3holes', 10, force=True, verbose=1)
Th = siMesh(meshfile, dim=3)
plt.close('all')
plt.ion()
DisplayFigures(nfig=2)
plt.figure(1)
siplt.plotmesh(Th, legend=True)
siplt.plotmesh(Th, d=1, color='black')
set_axes_equal()
plt.figure(2)
siplt.plotmesh(Th, d=2, labels=[10, 20, 21, 100, 101], legend=True)
set_axes_equal()
plt.axis('off')
return Th
def feval3D02():
meshfile = gmsh.buildmesh3d('cylinderkey', 15)
Th = siMesh(meshfile)
f = lambda x, y, z: 3 * x**2 - 2 * y**3 + 4 * z**2 - x * y
def g(x, y, z, a, b, c, d):
return a * x**2 + b * y**3 + c * z**2 + d * x * y
g1 = lambda x, y, z: g(x, y, z, 3, -2, 4, -1)
g2 = lambda X: g(X[0], X[1], X[2], 3, -2, 4, -1)
z = Th.feval(f)
z1 = Th.feval(g1)
z2 = Th.feval(g2)
print('max(abs(z1-z))=%e' % max(abs(z1 - z)))
print('max(abs(z2-z))=%e' % max(abs(z2 - z)))
def feval3D03():
meshfile = gmsh.buildmesh3d('cylinderkey', 15)
Th = siMesh(meshfile)
# f : R^3 -> R^2
f = [
lambda x, y, z: np.cos(2 * x) * np.sin(3 * y) - z,
lambda x, y, z: np.cos(3 * x) * np.sin(4 * y) + z
]
g = [
lambda X: np.cos(2 * X[0]) * np.sin(3 * X[1]) - X[2],
lambda x, y, z: np.cos(3 * x) * np.sin(4 * y) + z
]
V1 = Th.feval(f)
V2 = Th.feval(f)
print('V1.shape=' + str(V1.shape) + ' V2.shape=' + str(V2.shape))
print('max(abs(V1-V2))=%e' % np.max(np.abs(V1 - V2)))
def quiver3d01(N=10):
meshfile = gmsh.buildmesh3d('cylinder3dom', N, force=True)
plt.close('all')
Th = siMesh(meshfile)
u = Th.feval(lambda x, y, z: 3 * x**2 - y**3 + z**2 + x * y)
w = [
lambda x, y, z: y * np.cos(-(x**2 + y**2) / 10),
lambda x, y, z: -x * np.cos(-(x**2 + y**2) / 10), lambda x, y, z: z / 5
]
W = np.array([Th.feval(w[0]), Th.feval(w[1]), Th.feval(w[2])])
scale = 20
plt.ion()
DisplayFigures(nfig=4)
plt.figure(1)
sq = siplt.quiver(Th, W, nvec=3000, scale=scale)
siplt.plotmesh(Th, d=2, color='LightGray', alpha=0.05)
plt.colorbar(sq)
set_axes_equal()
plt.figure(2)
sq = siplt.quiver(Th, W, scalars=u, nvec=3000, scale=scale)
siplt.plotmesh(Th, d=2, color='LightGray', alpha=0.05)
plt.colorbar(sq)
plt.axis('off')
set_axes_equal()
plt.figure(3)
sq = siplt.quiver(Th, W, labels=[10, 11], nvec=3000, scale=scale)
siplt.plotmesh(Th, d=2, color='LightGray', alpha=0.05)
plt.axis('off')
set_axes_equal()
plt.colorbar(sq)
plt.figure(4)
sq = siplt.quiver(Th,
W,
scalars=u,
labels=[10, 11],
nvec=3000,
scale=scale)
siplt.plotmesh(Th, d=2, color='LightGray', alpha=0.05)
plt.axis('off')
set_axes_equal()
plt.colorbar(sq)
plt.show()
return Th
def feval3D01():
meshfile = gmsh.buildmesh3d('cylinderkey', 15)
Th = siMesh(meshfile)
g1 = lambda x, y, z: 3 * x**2 - y**3 + z**2 + x * y
g2 = lambda X: 3 * X[0]**2 - X[1]**3 + X[2]**2 + X[0] * X[1]
def g3(x, y, z):
return 3 * x**2 - y**3 + z**2 + x * y
def g4(X):
return 3 * X[0]**2 - X[1]**3 + X[2]**2 + X[0] * X[1]
z1 = Th.feval(g1)
z2 = Th.feval(g2)
z3 = Th.feval(g3)
z4 = Th.feval(g4)
print('max(abs(z2-z1))=%e' % max(abs(z2 - z1)))
print('max(abs(z3-z1))=%e' % max(abs(z3 - z1)))
print('max(abs(z4-z1))=%e' % max(abs(z4 - z1)))
def plot3d01(N=15):
meshfile = gmsh.buildmesh3d('cylinderkey', N)
Th = siMesh(meshfile)
plt.close('all')
plt.ion()
DisplayFigures(nfig=4)
u = Th.feval(lambda x, y, z: 3 * x**2 - y**3 + z**2 + x * y)
plt.figure(1)
h = siplt.plot(Th, u, s=2)
plt.colorbar(h)
plt.axis('off')
set_axes_equal()
plt.figure(2)
h2 = siplt.plot(Th, u, d=2, labels=[1000, 1020, 1021, 2000, 2020, 2021])
siplt.plot(Th,
u,
d=2,
labels=[10, 11, 31],
edgecolor='black',
linewidth=0.5)
plt.colorbar(h2)
plt.axis('off')
set_axes_equal()
plt.figure(3)
h2 = siplt.plot(Th, u, d=2, labels=[2000, 2020, 2021])
h1 = siplt.plot(Th, u, d=1, labels=[1075, 1077, 1078, 1081], linewidth=3)
siplt.plotmesh(Th, d=2, labels=[10, 11, 31], color='LightGray', alpha=0.2)
plt.colorbar(h1)
plt.axis('off')
set_axes_equal()
plt.figure(4)
siplt.plot(Th, u, d=2, labels=[1], alpha=0.1)
siplt.plot(Th, u, d=2, labels=[2000, 2020, 2021])
siplt.plot(Th, u, d=1, labels=[1075, 1077, 1078, 1081], linewidth=3)
siplt.plotmesh(Th, d=2, labels=[10, 11, 31], color='LightGray', alpha=0.2)
siplt.plotmesh(Th, d=1, labels=[1080, 1079], color='black', linewidth=2)
plt.axis('off')
set_axes_equal()
return Th