def __init__(self):
self.pde = SphereSinSinSinData()
self.surface = self.pde.domain()
self.mesh = self.pde.init_mesh(4)
node = self.mesh.entity('node')
cell = self.mesh.entity('cell')
self.tritree = Tritree(node, cell)
def grad_recovery_test(self, p=1, plot=False):
from fealpy.pde.surface_poisson_model_3d import SphereSinSinSinData
pde = SphereSinSinSinData()
surface = pde.domain()
mesh = pde.init_mesh()
for i in range(4):
space = SurfaceLagrangeFiniteElementSpace(mesh, surface, p=p)
uI = space.interpolation(pde.solution)
rg = space.grad_recovery(uI)
error0 = space.integralalg.L2_error(pde.solution, uI.value)
error1 = space.integralalg.L2_error(pde.gradient, rg.value)
def f(x):
return np.sum(rg.value(x)**2, axis=-1)
eta = space.integralalg.integral(f, celltype=True)
mesh.uniform_refine(surface=surface)
print(error1)
def interpolation(self, p=2, n=1, fname='surface.vtu'):
from fealpy.geometry import SphereSurface
from fealpy.pde.surface_poisson_model_3d import SphereSinSinSinData
pde = SphereSinSinSinData()
surface = pde.domain()
mesh = pde.init_mesh(n=n)
node = mesh.entity('node')
cell = mesh.entity('cell')
mesh = LagrangeTriangleMesh(node, cell, p=p, surface=surface)
space = ParametricLagrangeFiniteElementSpace(mesh, p=p)
uI = space.interpolation(pde.solution)
mesh.nodedata['uI'] = uI[:]
error0 = space.integralalg.error(pde.solution, uI.value)
error1 = space.integralalg.error(pde.gradient, uI.grad_value)
print(error0, error1)
mesh.to_vtk(fname=fname)
import pylab as pl
p = int(sys.argv[1])
maxit = int(sys.argv[2])
theta = 0.35
errorType = [
'$|| u_I - u_h ||_{l_2}$', '$|| u - u_h ||_{S,0}$',
'$||\\nabla_S u - \\nabla_S u_h||_{S,0}$'
]
Ndof = np.zeros((maxit, ), dtype=np.int)
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
integrator = TriangleQuadrature(3)
ralg = FEMFunctionRecoveryAlg()
pde = SphereSinSinSinData()
mesh = pde.init_mesh(2)
tmesh = Tritree(mesh.node, mesh.ds.cell, irule=1)
pmesh = tmesh.to_conformmesh()
fig = pl.figure()
axes = a3.Axes3D(fig)
pmesh.add_plot(axes)
for i in range(maxit):
print('step:', i)
fem = SurfacePoissonFEMModel(pmesh, pde, p, integrator)
fem.solve()
uh = fem.uh
rguh = ralg.harmonic_average(uh)
eta = fem.recover_estimate(rguh)
class TritreeTest:
def __init__(self):
self.pde = SphereSinSinSinData()
self.surface = self.pde.domain()
self.mesh = self.pde.init_mesh(4)
node = self.mesh.entity('node')
cell = self.mesh.entity('cell')
self.tritree = Tritree(node, cell)
def test_adaptive(self):
options = self.tritree.adaptive_options(maxrefine=1)
mesh = self.tritree.to_conformmesh()
for i in range(1):
space = SurfaceLagrangeFiniteElementSpace(mesh, self.surface, p=1)
uI = space.interpolation(self.pde.solution)
phi = lambda x: uI.grad_value(x)**2
eta = space.integralalg.integral(lambda x: uI.grad_value(x)**2,
celltype=True,
barycenter=True)
eta = eta.sum(axis=-1)
self.tritree.adaptive(eta, options, surface=self.surface)
mesh = self.tritree.to_conformmesh()
print(self.tritree.celldata['idxmap'])
cell = self.tritree.entity('cell')
print(cell[15])
cell = mesh.entity('cell')
print(cell[104])
print(cell[140])
fig = pl.figure()
axes = a3.Axes3D(fig)
self.tritree.add_plot(axes)
plt.show()
def test_interpolation_surface(self, p=1):
options = self.tritree.adaptive_options(maxrefine=1, p=p)
mesh = self.tritree.to_conformmesh()
space = SurfaceLagrangeFiniteElementSpace(mesh, self.surface, p=p)
uI = space.interpolation(self.pde.solution)
print('1:', space.number_of_global_dofs())
print('2:', uI.shape)
error0 = space.integralalg.L2_error(self.pde.solution, uI)
print(error0)
data = self.tritree.interpolation(uI)
print('3', data.shape)
options['data'] = {'q': data}
if 1:
eta = space.integralalg.integral(lambda x: uI.grad_value(x)**2,
celltype=True,
barycenter=True)
eta = eta.sum(axis=-1)
self.tritree.adaptive(eta, options, surface=self.surface)
else:
self.tritree.uniform_refine(options=options, surface=self.surface)
mesh = self.tritree.to_conformmesh(options)
space = SurfaceLagrangeFiniteElementSpace(mesh, self.surface, p=p)
data = options['data']['q']
print('data:', data.shape)
uh = space.to_function(data)
print('uh:', uh.shape)
error1 = space.integralalg.L2_error(self.pde.solution, uh)
print(error1)
uI = space.interpolation(self.pde.solution)
error2 = space.integralalg.L2_error(self.pde.solution, uI)
print(error2)
data = self.tritree.interpolation(uI)
options['data'] = {'q': data}
if 0:
eta = space.integralalg.integral(lambda x: uI.grad_value(x)**2,
celltype=True,
barycenter=True)
eta = eta.sum(axis=-1)
self.tritree.adaptive(eta, options, surface=self.surface)
else:
self.tritree.uniform_refine(options=options, surface=self.surface)
mesh = self.tritree.to_conformmesh(options)
space = SurfaceLagrangeFiniteElementSpace(mesh, self.surface, p=p)
data = options['data']['q']
uh = space.to_function(data)
error3 = space.integralalg.L2_error(self.pde.solution, uh)
print(error3)
if 0:
fig = pl.figure()
axes = a3.Axes3D(fig)
self.tritree.add_plot(axes)
plt.show()
else:
fig = pl.figure()
axes = a3.Axes3D(fig)
mesh.add_plot(axes)
plt.show()
def test_interpolation_plane(self):
def u(p):
x = p[..., 0]
y = p[..., 1]
return x * y
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float)
cell = np.array([(1, 2, 0), (3, 0, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
node = mesh.entity('node')
cell = mesh.entity('cell')
tritree = Tritree(node, cell)
mesh = tritree.to_conformmesh()
space = LagrangeFiniteElementSpace(mesh, p=2)
uI = space.interpolation(u)
error0 = space.integralalg.L2_error(u, uI)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, node=space.interpolation_points(), showindex=True)
data = tritree.interpolation(uI)
options = tritree.adaptive_options(method='numrefine',
data={"q": data},
maxrefine=1,
p=2)
if 1:
#eta = space.integralalg.integral(lambda x : uI.grad_value(x)**2, celltype=True, barycenter=True)
#eta = eta.sum(axis=-1)
eta = np.array([1, 0], dtype=np.int)
tritree.adaptive(eta, options)
else:
tritree.uniform_refine(options=options)
fig = plt.figure()
axes = fig.gca()
tritree.add_plot(axes)
tritree.find_node(axes, showindex=True)
mesh = tritree.to_conformmesh(options)
space = LagrangeFiniteElementSpace(mesh, p=2)
data = options['data']['q']
uh = space.to_function(data)
error1 = space.integralalg.L2_error(u, uh)
data = tritree.interpolation(uh)
isLeafCell = tritree.is_leaf_cell()
fig = plt.figure()
axes = fig.gca()
tritree.add_plot(axes)
tritree.find_node(axes,
node=space.interpolation_points(),
showindex=True)
tritree.find_cell(axes, index=isLeafCell, showindex=True)
options = tritree.adaptive_options(method='numrefine',
data={"q": data},
maxrefine=1,
maxcoarsen=1,
p=2)
if 1:
#eta = space.integralalg.integral(lambda x : uI.grad_value(x)**2, celltype=True, barycenter=True)
#eta = eta.sum(axis=-1)
eta = np.array([-1, -1, -1, -1, 0, 1], dtype=np.int)
tritree.adaptive(eta, options)
else:
tritree.uniform_refine(options=options)
mesh = tritree.to_conformmesh(options)
space = LagrangeFiniteElementSpace(mesh, p=2)
data = options['data']['q']
uh = space.to_function(data)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, node=space.interpolation_points(), showindex=True)
mesh.find_cell(axes, showindex=True)
error2 = space.integralalg.L2_error(u, uh)
print(error0)
print(error1)
print(error2)
plt.show()
import pylab as pl
p = int(sys.argv[1])
maxit = int(sys.argv[2])
theta = 0.4
errorType = [
'$|| u_I - u_h ||_{l_2}$', '$|| u - u_h ||_{S,0}$',
'$||\\nabla_S u - \\nabla_S u_h||_{S,0}$'
]
Ndof = np.zeros((maxit, ), dtype=np.int)
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
integrator = TriangleQuadrature(3)
ralg = FEMFunctionRecoveryAlg()
pde = SphereSinSinSinData()
surface = Sphere()
mesh = surface.init_mesh()
mesh.uniform_refine(n=2, surface=surface)
tmesh = Tritree(mesh.node, mesh.ds.cell, irule=1)
pmesh = tmesh.to_conformmesh()
fig = pl.figure()
axes = a3.Axes3D(fig)
pmesh.add_plot(axes)
for i in range(maxit):
print('step:', i)
fem = SurfacePoissonFEMModel(pmesh, pde, p, integrator)
fem.solve()
uh = fem.uh