def continuation_2D(nx=4, interactive=False):
dim = 2
dof = 3
ny = nx
nz = 1
parameters = {'Reynolds Number': 0}
interface = Interface(parameters, nx, ny, nz, dim, dof)
continuation = Continuation(interface, parameters)
x0 = numpy.zeros(dof * nx * ny * nz)
x0 = continuation.newton(x0)
target = 2000
ds = 100
maxit = 20
x = continuation.continuation(x0, 'Reynolds Number', target, ds, maxit)
assert numpy.linalg.norm(x) > 0
if not interactive:
return x
print(x)
x = plot_utils.create_state_mtx(x, nx, ny, nz, dof)
plot_utils.plot_state(x[:, :, 0, 0], x[:, :, 0, 1], nx, ny)
def test_continuation_Bratu_problem(para, ds, nx=4, interactive=False):
dim = 1
dof = 1
ny = 1
nz = 1
parameters = para
interface = Interface(parameters, nx, ny, nz, dim, dof)
continuation = Continuation(interface, parameters)
x0 = numpy.zeros(dof * (nx-1) * ny * nz)
x0 = continuation.newton(x0)
target = 3
ds = ds
maxit = int(4 / ds * 2) * 100
(x, para, u, u_norm, C_v, iterations) = continuation.continuation(x0, 'Bratu parameter', target, ds, maxit)
# print(para[200])
# plt.plot(interface.discretization.x[0:15], u[200])
# plt.xlabel('x')
# plt.ylabel('u(x)')
# plt.show()
assert numpy.linalg.norm(x) > 0
# if not interactive:
# return
# print(x)
return para, u, u_norm, C_v, iterations
def test_continuation(nx=4, interactive=False):
dim = 3
dof = 4
ny = nx
nz = nx
parameters = {}
interface = Interface(parameters, nx, ny, nz, dim, dof)
continuation = Continuation(interface, parameters)
x0 = numpy.zeros(dof * nx * ny * nz)
x0 = continuation.newton(x0)
start = 0
target = 100
ds = 100
x = continuation.continuation(x0, 'Reynolds Number', start, target, ds)[0]
assert numpy.linalg.norm(x) > 0
if not interactive:
return
print(x)
x = plot_utils.create_state_mtx(x, nx, ny, nz, dof)
plot_utils.plot_velocity_magnitude(x[:, ny // 2, :, 0], x[:, ny // 2, :,
2], nx, nz)
def test_continuation_2D_stretched(nx=4, interactive=False):
dim = 2
dof = 3
ny = nx
nz = 1
xpos = utils.create_stretched_coordinate_vector(0, 1, nx, 1.5)
ypos = utils.create_stretched_coordinate_vector(0, 1, ny, 1.5)
parameters = {}
interface = Interface(parameters, nx, ny, nz, dim, dof, xpos, ypos)
continuation = Continuation(interface, parameters)
x0 = numpy.zeros(dof * nx * ny * nz)
x0 = continuation.newton(x0)
start = 0
target = 2000
ds = 100
x = continuation.continuation(x0, 'Reynolds Number', start, target, ds)[0]
assert numpy.linalg.norm(x) > 0
if not interactive:
return x
print(x)
x = plot_utils.create_state_mtx(x, nx, ny, nz, dof)
plot_utils.plot_velocity_magnitude(x[:, :, 0, 0], x[:, :, 0, 1], interface)
def HYMLS_Bratu_problem(nx=8, interactive=False):
try:
from fvm import HYMLSInterface
from PyTrilinos import Epetra
from PyTrilinos import Teuchos
except ImportError:
pytest.skip("HYMLS not found")
dim = 1
dof = 1
ny = 1
nz = 1
parameters = Teuchos.ParameterList()
parameters.set('Bratu parameter', 0)
parameters.set('Bordered Solver', True)
parameters.set('Problem Type', 'Bratu problem')
comm = Epetra.PyComm()
interface = HYMLSInterface.Interface(comm, parameters, nx, ny, nz, dim,
dof)
m = interface.map
continuation = Continuation(interface, parameters)
x0 = HYMLSInterface.Vector(m)
x0.PutScalar(0.0)
x0 = continuation.newton(x0)
target = 3
ds = 0.1
maxit = int(3.6 / ds * 2)
(x, paras, u) = continuation.continuation(x0, 'Bratu parameter', target,
ds, maxit)
assert x.Norm2() > 0
if not interactive:
return
x = gather(x)
if comm.MyPID() == 0:
print(x)
# x = plot_utils.create_state_mtx(x, nx, ny, nz, dof)
# plot_utils.plot_state(x[:, :, 0, 0], x[:, :, 0, 1], nx, ny)
plt.plot(paras, u)
plt.title('nx = ' + repr(nx))
plt.xlabel('Bratu parameter C')
plt.ylabel('Infinity Norm of u(x)')
plt.show()
def x(interface):
from fvm import HYMLSInterface
continuation = Continuation(interface, interface.parameters)
x0 = HYMLSInterface.Vector(interface.map)
x0 = continuation.newton(x0)
start = 0
target = 2000
ds = 100
return continuation.continuation(x0, 'Reynolds Number', start, target, ds)[0]
def test_HYMLS_2D_stretched(nx=8, interactive=False):
try:
from fvm import HYMLSInterface
from PyTrilinos import Epetra
from PyTrilinos import Teuchos
except ImportError:
pytest.skip("HYMLS not found")
dim = 3
dof = 4
ny = nx
nz = 1
parameters = Teuchos.ParameterList()
parameters.set('Reynolds Number', 0)
parameters.set('Bordered Solver', True)
parameters.set('Grid Stretching', True)
parameters.set('Verbose', True)
comm = Epetra.PyComm()
interface = HYMLSInterface.Interface(comm, parameters, nx, ny, nz, dim,
dof)
m = interface.map
continuation = Continuation(interface, parameters)
x0 = HYMLSInterface.Vector(m)
x0.PutScalar(0.0)
x0 = continuation.newton(x0)
start = 0
target = 2000
ds = 100
x = continuation.continuation(x0, 'Reynolds Number', start, target, ds)[0]
assert x.Norm2() > 0
if not interactive:
return
x = gather(x)
if comm.MyPID() == 0:
print(x)
xpos = utils.create_stretched_coordinate_vector(0, 1, nx, 1.5)
ypos = utils.create_stretched_coordinate_vector(0, 1, ny, 1.5)
x = plot_utils.create_velocity_magnitude_mtx(x, nx, ny, nz, dof)
plot_utils.plot_velocity_magnitude(x[:, :, 0, 0],
x[:, :, 0, 1],
x=xpos,
y=ypos)
def numpy_x(numpy_interface):
n = numpy_interface.dof * numpy_interface.nx * numpy_interface.ny * numpy_interface.nz
parameters = {}
continuation = Continuation(numpy_interface, parameters)
x0 = numpy.zeros(n)
x0 = continuation.newton(x0)
start = 0
target = 2000
ds = 100
return continuation.continuation(x0, 'Reynolds Number', start, target,
ds)[0]
def solve_nonlinear_system(para, nx=4):
dim = 1
dof = 1
ny = 1
nz = 1
parameters = para
interface = Interface(parameters, nx, ny, nz, dim, dof)
continuation = Continuation(interface, parameters)
x0 = np.zeros(dof * (nx - 1) * ny * nz)
x0 = continuation.newton(x0)
return x0
def test_continuation_time_integration(nx=4, interactive=False):
dim = 2
dof = 3
ny = nx
nz = 1
parameters = {'Newton Tolerance': 1e-6}
interface = Interface(parameters, nx, ny, nz, dim, dof)
continuation = Continuation(interface, parameters)
x0 = numpy.zeros(dof * nx * ny * nz)
x0 = continuation.newton(x0)
start = 0
target = 2000
ds = 100
x = continuation.continuation(x0, 'Reynolds Number', start, target, ds)[0]
# Start from a perturbed solution
x2 = utils.create_state_mtx(x, nx, ny, nz, dof)
x2[1:nx - 1, 1:ny - 1, :, 0] += 0.1 * numpy.random.random(
(nx - 2, ny - 2, nz))
x2 = utils.create_state_vec(x2, nx, ny, nz, dof)
assert numpy.linalg.norm(x[0:len(x):dof] - x2[0:len(x):dof]) > 1e-2
assert numpy.linalg.norm(x[1:len(x):dof] - x2[1:len(x):dof]) < 1e-4
time_integration = TimeIntegration(interface, parameters)
x3 = time_integration.integration(x2, 1, 1)[0]
assert numpy.linalg.norm(x[0:len(x):dof] - x3[0:len(x):dof]) > 1e-2
assert numpy.linalg.norm(x[1:len(x):dof] - x3[1:len(x):dof]) > 1e-2
time_integration = TimeIntegration(interface, parameters)
x3 = time_integration.integration(x2, 100, 1000)[0]
assert numpy.linalg.norm(x[0:len(x):dof] - x3[0:len(x):dof]) < 1e-4
assert numpy.linalg.norm(x[1:len(x):dof] - x3[1:len(x):dof]) < 1e-4
# Start from zero
x2[:] = 0
time_integration = TimeIntegration(interface, parameters)
x3 = time_integration.integration(x2, 100, 1000)[0]
assert numpy.linalg.norm(x[0:len(x):dof] - x3[0:len(x):dof]) < 1e-4
assert numpy.linalg.norm(x[1:len(x):dof] - x3[1:len(x):dof]) < 1e-4