def plot2d01(N=25):
meshfile = gmsh.buildmesh2d('condenser11', N)
Th = siMesh(meshfile)
u = Th.feval(
lambda x, y: 5 * np.exp(-3 * (x**2 + y**2)) * np.cos(x) * np.sin(y))
plt.rcParams['text.usetex'] = True
plt.rcParams['text.latex.unicode'] = True
plt.close('all')
plt.ion()
DisplayFigures(nfig=4)
fig = plt.figure(1)
siplt.plot(Th, u)
plt.colorbar()
set_axes_equal()
plt.figure(2)
siplt.plot(Th, u, labels=[20, 2, 4, 6, 8])
siplt.plotmesh(Th, labels=10, color='LightGray')
set_axes_equal()
plt.axis('off')
plt.figure(3)
#plt.set_cmap(plt.cm.get_cmap(name='jet'))
h = siplt.plot(Th, u, plane=False, colormap='jet')
siplt.plotmesh(Th, d=1, color='Black', z=u)
plt.colorbar(h)
set_axes_equal()
plt.figure(4)
h = siplt.plot(Th, u, d=1, plane=False, linewidth=3)
plt.colorbar(h)
siplt.plotmesh(Th, labels=10, color='LightGray', z=u)
set_axes_equal()
plt.axis('off')
return Th
def plotmesh2d01():
meshfile = gmsh.buildmesh2d('disk5holes.geo', 20, force=True, verbose=1)
Th = siMesh(meshfile, dim=2)
plt.close('all')
plt.ion()
DisplayFigures(nfig=2)
plt.figure(1)
siplt.plotmesh(Th, legend=True)
set_axes_equal()
plt.figure(2)
siplt.plotmesh(Th, color='LightGray')
siplt.plotmesh(Th, d=1, linewidth=2, legend=True)
plt.axis('off')
set_axes_equal()
return Th
def plotiso2d01(N=15):
meshfile = gmsh.buildmesh2d('condenser11', N)
Th = siMesh(meshfile)
u = Th.feval(
lambda x, y: 5 * np.exp(-3 * (x**2 + y**2)) * np.cos(x) * np.sin(y))
plt.close('all')
plt.ion()
DisplayFigures(nfig=4)
fig = plt.figure(1)
siplt.plotiso(Th, u, niso=15)
siplt.plotmesh(Th, d=1, color='Black')
set_axes_equal()
plt.colorbar()
fig = plt.figure(2)
isos = np.linspace(-1, 1, 21)
siplt.plotiso(Th,
u,
niso=15,
color='LightGray',
isorange=isos,
linestyles=':')
siplt.plotmesh(Th, d=1, color='Black')
plt.axis('off')
set_axes_equal()
fig = plt.figure(3)
siplt.plotiso(Th, u, labels=10, niso=15, linewidths=1)
plt.colorbar()
siplt.plotmesh(Th, labels=10, color='LightGray', linewidth=1, alpha=0.05)
siplt.plotiso(Th,
u,
labels=[2, 4, 6, 8, 20],
niso=15,
color='Gray',
linewidths=1)
siplt.plot(Th, u, labels=[2, 4, 6, 8, 20])
siplt.plotiso(Th, u, isorange=0, color='Black', linewidths=2)
plt.axis('off')
set_axes_equal()
fig = plt.figure(4)
siplt.plotiso(Th, u, labels=10, niso=15, linewidths=1, color='White')
siplt.plot(Th, u, labels=10)
siplt.plotiso(Th, u, labels=[2, 4, 6, 8, 20], niso=15, linewidths=1)
cb = plt.colorbar()
cb.lines[0].set_linewidth(4)
plt.axis('off')
set_axes_equal()
return Th
def feval2D02():
meshfile = gmsh.buildmesh2d('condenser11', 50)
Th = siMesh(meshfile)
f = lambda x, y: np.cos(2 * x) * np.sin(3 * y)
def g(x, y, cx, cy):
return np.cos(cx * x) * np.sin(cy * y)
g1 = lambda x, y: g(x, y, 2, 3)
g2 = lambda X: g(X[0], X[1], 2, 3)
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 quiver2d01(N=15):
meshfile = gmsh.buildmesh2d('condenser11', N)
plt.close('all')
DisplayFigures(nfig=4)
Th = siMesh(meshfile)
u = Th.feval(
lambda x, y: 5 * np.exp(-3 * (x**2 + y**2)) * np.cos(x) * np.sin(y))
w = [
lambda x, y: y * np.cos(-(x**2 + y**2) / 10),
lambda x, y: -x * np.cos(-(x**2 + y**2) / 10)
]
W = np.array([Th.feval(w[0]), Th.feval(w[1])])
plt.ion()
plt.figure(1)
siplt.quiver(Th, W, scale=50, nvec=3000)
siplt.plotmesh(Th, d=1, color='black')
set_axes_equal()
plt.colorbar()
plt.figure(2)
siplt.quiver(Th, W, scalars=u, scale=50, nvec=3000)
siplt.plotmesh(Th, d=1, color='black')
plt.axis('off')
set_axes_equal()
plt.colorbar()
plt.figure(3)
siplt.quiver(Th, W, labels=[2, 4, 6, 8, 20], nvec=1000, scale=50)
siplt.plotmesh(Th, d=1, color='black')
plt.axis('off')
set_axes_equal()
plt.colorbar()
plt.figure(4)
siplt.quiver(Th,
W,
labels=[2, 4, 6, 8, 20],
scalars=u,
scale=50,
nvec=1000)
siplt.plotmesh(Th, d=1, color='black')
plt.axis('off')
set_axes_equal()
plt.colorbar()
plt.show()
return Th
def feval2D03():
meshfile = gmsh.buildmesh2d('condenser11', 50)
Th = siMesh(meshfile)
# f : R^2 -> R^3
f = [
lambda x, y: np.cos(2 * x) * np.sin(3 * y),
lambda x, y: np.cos(3 * x) * np.sin(4 * y),
lambda x, y: np.cos(4 * x) * np.sin(5 * y)
]
g = [
lambda X: np.cos(2 * X[0]) * np.sin(3 * X[1]),
lambda x, y: np.cos(3 * x) * np.sin(4 * y),
lambda x, y: np.cos(4 * X[0]) * np.sin(5 * X[1])
]
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 feval2D01():
meshfile = gmsh.buildmesh2d('condenser11', 50)
Th = siMesh(meshfile)
g1 = lambda x, y: np.cos(x) * np.sin(y)
g2 = lambda X: np.cos(X[0]) * np.sin(X[1])
def g3(x, y):
return np.cos(x) * np.sin(y)
def g4(X):
return np.cos(X[0]) * np.sin(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 find2D01():
meshfile = gmsh.buildmesh2d('condenser11', 50)
Th = siMesh(meshfile)
print('*** 1: print mesh')
print(Th)
print('*** 2: print labels of the 2-simplex elementary meshes')
idx = Th.find(2)
print('d=2, labels=' + str(Th.sThlab[idx]))
print('*** 3: print labels of the 1-simplex elementary meshes')
idx = Th.find(1)
print('d=1, labels=' + str(Th.sThlab[idx]))
d = 2
lab = 6
print('*** 4: 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 = 101
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]))