def test_brusselator2d():
problem = Brusselator2d()
n = problem.mesh.control_volumes.shape[0]
u0 = np.zeros((2, n))
b0 = 0.0
plt.ion()
fig = plt.figure()
ax = fig.add_subplot(111)
plt.axis("square")
plt.xlabel("b")
plt.ylabel("$||u||_\\infty$")
b_list = []
values_list = []
(line1,) = ax.plot(b_list, values_list, "-", color="#1f77f4")
def callback(k, b, sol):
b_list.append(b)
line1.set_xdata(b_list)
values_list.append(np.max(np.abs(sol)))
line1.set_ydata(values_list)
ax.set_xlim(0.0, 200.0)
ax.set_ylim(0.0, 40.0)
fig.canvas.draw()
fig.canvas.flush_events()
# Store the solution
u, v = sol
meshio.write_points_cells(
f"sol{k:03d}.vtk",
problem.mesh.points,
{"triangle": problem.mesh.cells["points"]},
point_data={"u": u, "v": v},
)
pacopy.natural(problem, u0, b0, callback, max_steps=100)
def test_allen_cahn():
problem = AllenCahn()
n = problem.mesh.control_volumes.shape[0]
u0 = numpy.zeros(n, dtype=float)
# delta0 = 0.04
delta0 = 0.2
plt.ion()
fig = plt.figure()
ax = fig.add_subplot(111)
plt.axis("square")
plt.xlabel("$\\mu$")
plt.ylabel("$||u||_2^2 / |\\Omega|$")
plt.grid()
b_list = []
values_list = []
(line1, ) = ax.plot(b_list, values_list, "-", color="#1f77f4")
area = numpy.sum(problem.mesh.control_volumes)
def callback(k, b, sol):
b_list.append(b)
line1.set_xdata(b_list)
values_list.append(problem.inner(sol, sol) / area)
line1.set_ydata(values_list)
ax.set_xlim(0.0, 1.0)
ax.set_ylim(0.0, 1.0)
ax.invert_yaxis()
fig.canvas.draw()
fig.canvas.flush_events()
# Store the solution
meshio.write_points_cells(
f"sol{k:03d}.vtk",
problem.mesh.node_coords,
{"triangle": problem.mesh.cells["nodes"]},
point_data={"u": sol},
)
# input("Press")
pacopy.natural(
problem,
u0,
delta0,
callback,
max_steps=6,
lambda_stepsize0=-1.0e-1,
max_newton_steps=16,
newton_tol=1.0e-10,
)
def solve(self):
if self.cont_method == 'Euler-Newton':
pacopy.euler_newton(self,
self.u0,
self.lmbda0,
self.callback,
max_steps=self.max_steps,
newton_tol=self.newton_tol)
elif self.cont_method == 'Natural':
pacopy.natural(self,
self.u0,
self.lmbda0,
self.callback,
max_steps=self.max_steps,
newton_tol=self.newton_tol)
reynolds: float,
uvp: np.ndarray,
milestones=Iterable[float]):
"""Echo the Reynolds number and plot streamlines at milestones"""
print(f'Re = {reynolds}')
if reynolds in milestones:
psi[reynolds] = bfs.streamfunction(bfs.split(uvp)[0])
if __name__ == '__main__':
ax = bfs.streamlines(psi[reynolds])
ax.set_title(f'Re = {reynolds}')
ax.get_figure().savefig(Path(__file__).with_name(
f'{Path(__file__).stem}-{reynolds}-psi.png'),
bbox_inches="tight",
pad_inches=0)
if __name__ == '__main__':
milestones = [50., 150., 450., 750.]
else:
milestones = [50.]
natural(bfs,
bfs.make_vector(),
0.,
partial(callback, milestones=milestones),
lambda_stepsize0=50.,
milestones=milestones)
def test_bratu(max_steps=10, update_plot=False):
problem = Bratu1d()
u0 = numpy.zeros(problem.n)
lmbda0 = 0.0
# https://stackoverflow.com/a/4098938/353337
plt.ion()
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 5))
# fig = plt.figure()
ax1 = fig.add_subplot(1, 2, 1)
ax1.set_xlabel("$\\lambda$")
ax1.set_ylabel("$||u||_2$")
ax1.set_xlim(0.0, 4.0)
ax1.set_ylim(0.0, 6.0)
ax1.grid()
(line1, ) = ax1.plot([], [], "-x", color="C0")
ax2 = fig.add_subplot(1, 2, 2)
ax2.set_title("solution")
ax2.set_xlim(0.0, 1.0)
ax2.set_ylim(0.0, 5.0)
ax2.grid()
(line2, ) = ax2.plot([], [], "-", color="C0")
line2.set_xdata(numpy.linspace(0.0, 1.0, problem.n))
# line3, = ax2.plot([], [], "-", color="C1")
# line3.set_xdata(numpy.linspace(0.0, 1.0, problem.n))
milestones = numpy.arange(0.5, 3.2, 0.5)
def callback(k, lmbda, sol):
if update_plot:
line1.set_xdata(numpy.append(line1.get_xdata(), lmbda))
# val = numpy.max(numpy.abs(sol))
val = numpy.sqrt(problem.inner(sol, sol))
line1.set_ydata(numpy.append(line1.get_ydata(), val))
# ax1.plot(
# [lmbda_pre], [numpy.sqrt(problem.inner(u_pre, u_pre))], ".", color="C1"
# )
line2.set_ydata(sol)
# line3.set_ydata(du_dlmbda)
fig.canvas.draw()
fig.canvas.flush_events()
# plt.savefig('bratu1d.png', transparent=True, bbox_inches="tight")
pacopy.natural(
problem,
u0,
lmbda0,
callback,
max_steps=max_steps,
newton_tol=1e-10,
milestones=milestones,
)
# The condition number of the Jacobian is about 10^4, so we can only expect Newton
# to converge up to about this factor above machine precision.
pacopy.euler_newton(problem,
u0,
lmbda0,
callback,
max_steps=max_steps,
newton_tol=1.0e-10)
bfs = BackwardFacingStep(lcar=.2)
def callback(_: int,
reynolds: float,
uvp: np.ndarray,
name: str,
milestones=Iterable[float]):
"""Echo the Reynolds number and plot streamlines at milestones"""
print(f'Re = {reynolds}')
if reynolds in milestones:
ax = bfs.streamlines(bfs.streamfunction(bfs.split(uvp)[0]))
ax.set_title(f'Re = {reynolds}')
ax.get_figure().savefig(f'{name}-{reynolds}-psi.png',
bbox_inches="tight", pad_inches=0)
if __name__ == '__main__':
from os.path import splitext
from sys import argv
milestones = [50., 150., 450., 750.]
natural(bfs, bfs.make_vector(), 0.,
partial(callback,
name=splitext(argv[0])[0],
milestones=milestones),
lambda_stepsize0=50.,
milestones=milestones)
def test_bratu(max_steps=10, update_plot=False):
problem = Bratu1d()
u0 = numpy.zeros(problem.n)
lmbda0 = 0.0
plt.ion()
fig = plt.figure()
ax1 = fig.add_subplot(111)
ax1.set_xlabel("$\\lambda$")
ax1.set_ylabel("$||u||_2$")
ax1.grid()
# ax2 = fig.add_subplot(122)
# ax2.grid()
(line1,) = ax1.plot([], [], "-x", color="#1f77f4")
# line2, = ax2.plot([], [], "-", color="#1f77f4")
# line2.set_xdata(numpy.linspace(0.0, 1.0, problem.n))
# line3, = ax2.plot([], [], "-", color="red")
# line3.set_xdata(numpy.linspace(0.0, 1.0, problem.n))
milestones = numpy.arange(0.5, 3.2, 0.5)
if update_plot:
profile_fig, profile_ax = plt.subplots()
def callback(k, lmbda, sol):
if update_plot:
line1.set_xdata(numpy.append(line1.get_xdata(), lmbda))
# val = numpy.max(numpy.abs(sol))
val = numpy.sqrt(problem.inner(sol, sol))
line1.set_ydata(numpy.append(line1.get_ydata(), val))
ax1.set_xlim(0.0, 4.0)
ax1.set_ylim(0.0, 6.0)
# ax1.plot([lmbda_pre], [numpy.sqrt(problem.inner(u_pre, u_pre))], ".r")
# line2.set_ydata(sol)
# line3.set_ydata(du_dlmbda)
# ax2.set_xlim(0.0, 1.0)
# ax2.set_ylim(0.0, 6.0)
fig.canvas.draw()
fig.canvas.flush_events()
# plt.savefig('bratu1d.png', transparent=True, bbox_inches="tight")
if lmbda in milestones:
profile_ax.plot(numpy.linspace(0.0, 1.0, problem.n), sol, label=lmbda)
pacopy.natural(
problem,
u0,
lmbda0,
callback,
max_steps=max_steps,
newton_tol=1e-10,
milestones=milestones,
)
# The condition number of the Jacobian is about 10^4, so we can only expect Newton
# to converge up to about this factor above machine precision.
pacopy.euler_newton(
problem, u0, lmbda0, callback, max_steps=max_steps, newton_tol=1.0e-10
)