def u_P1():
"""
Plot P1 basis functions and a resulting u to
illustrate what it means to use finite elements.
"""
import matplotlib.pyplot as plt
x = [0, 1.5, 2.5, 3.5, 4]
phi = [np.zeros(len(x)) for i in range(len(x)-2)]
for i in range(len(phi)):
phi[i][i+1] = 1
#u = 5*x*np.exp(-0.25*x**2)*(4-x)
u = [0, 8, 5, 4, 0]
for i in range(len(phi)):
plt.plot(x, phi[i], 'r-') #, label=r'$\varphi_%d$' % i)
plt.text(x[i+1], 1.2, r'$\varphi_%d$' % i)
plt.plot(x, u, 'b-', label='$u$')
plt.legend(loc='upper left')
plt.axis([0, x[-1], 0, 9])
plt.savefig('tmp_u_P1.png')
plt.savefig('tmp_u_P1.pdf')
# Mark elements
for xi in x[1:-1]:
plt.plot([xi, xi], [0, 9], 'm--')
# Mark nodes
#plt.plot(x, np.zeros(len(x)), 'ro', markersize=4)
plt.savefig('tmp_u_P1_welms.png')
plt.savefig('tmp_u_P1_welms.pdf')
plt.show()
def u_P1():
"""
Plot P1 basis functions and a resulting u to
illustrate what it means to use finite elements.
"""
import matplotlib.pyplot as plt
x = [0, 1.5, 2.5, 3.5, 4]
phi = [np.zeros(len(x)) for i in range(len(x)-2)]
for i in range(len(phi)):
phi[i][i+1] = 1
#u = 5*x*np.exp(-0.25*x**2)*(4-x)
u = [0, 8, 5, 4, 0]
for i in range(len(phi)):
plt.plot(x, phi[i], 'r-') #, label=r'$\varphi_%d$' % i)
plt.text(x[i+1], 1.2, r'$\varphi_%d$' % i)
plt.plot(x, u, 'b-', label='$u$')
plt.legend(loc='upper left')
plt.axis([0, x[-1], 0, 9])
plt.savefig('u_example_P1.png')
plt.savefig('u_example_P1.pdf')
# Mark elements
for xi in x[1:-1]:
plt.plot([xi, xi], [0, 9], 'm--')
# Mark nodes
#plt.plot(x, np.zeros(len(x)), 'ro', markersize=4)
plt.savefig('u_example_P1_welms.png')
plt.savefig('u_example_P1_welms.pdf')
plt.show()
def plot_boundaries(outer_boundary, inner_boundaries=[], marked_points=None):
if not isinstance(inner_boundaries, (tuple, list)):
inner_boundaries = [inner_boundaries]
boundaries = [outer_boundary]
boundaries.extend(inner_boundaries)
# Find max/min of plotting area
plot_area = [
min([b.x.min() for b in boundaries]),
max([b.x.max() for b in boundaries]),
min([b.y.min() for b in boundaries]),
max([b.y.max() for b in boundaries]),
]
aspect = (plot_area[3] - plot_area[2]) / (plot_area[1] - plot_area[0])
for b in boundaries:
plot(b.x, b.y, daspect=[aspect, 1, 1], daspectratio="manual")
hold("on")
axis(plot_area)
title("Specification of domain with %d boundaries" % len(boundaries))
if marked_points:
for pt, name in marked_points:
text(pt[0], pt[1], name)
def plot_boundaries(outer_boundary, inner_boundaries=[], marked_points=None):
if not isinstance(inner_boundaries, (tuple, list)):
inner_boundaries = [inner_boundaries]
boundaries = [outer_boundary]
boundaries.extend(inner_boundaries)
# Find max/min of plotting area
plot_area = [
min([b.x.min() for b in boundaries]),
max([b.x.max() for b in boundaries]),
min([b.y.min() for b in boundaries]),
max([b.y.max() for b in boundaries])
]
aspect = (plot_area[3] - plot_area[2]) / (plot_area[1] - plot_area[0])
for b in boundaries:
plot(b.x, b.y, daspect=[aspect, 1, 1], daspectratio='manual')
hold('on')
axis(plot_area)
title('Specification of domain with %d boundaries' % len(boundaries))
if marked_points:
for pt, name in marked_points:
text(pt[0], pt[1], name)
