def __init__(self, scale=2):
self.scale = scale
self.pde = HeartSurfacetData()
self.surface = self.pde.domain()
self.mesh = self.pde.init_mesh()
self.mesh.uniform_refine(surface=self.surface)
node = self.mesh.entity('node')
cell = self.mesh.entity('cell')
self.tritree = Tritree(node, cell)
def mesh_scale_test(self, plot=True):
scale = 10
pde = HeartSurfacetData()
surface = pde.domain()
mesh = pde.init_mesh()
space = SurfaceLagrangeFiniteElementSpace(mesh,
surface,
p=1,
scale=scale)
mesh = space.mesh
if plot is True:
fig = plt.figure()
axes = Axes3D(fig)
mesh.add_plot(axes, showaxis=True)
plt.show()
class HeartTritreeTest:
def __init__(self, scale=2):
self.scale = scale
self.pde = HeartSurfacetData()
self.surface = self.pde.domain()
self.mesh = self.pde.init_mesh()
self.mesh.uniform_refine(surface=self.surface)
node = self.mesh.entity('node')
cell = self.mesh.entity('cell')
self.tritree = Tritree(node, cell)
def test_interpolation_surface(self, p=1):
options = self.tritree.adaptive_options(maxrefine=1, p=p)
mesh = self.tritree.to_conformmesh()
fig = pl.figure()
axes = a3.Axes3D(fig)
mesh.add_plot(axes, showaxis=True)
space = SurfaceLagrangeFiniteElementSpace(mesh,
self.surface,
p=p,
scale=self.scale)
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 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)
fig = pl.figure()
axes = a3.Axes3D(fig)
self.tritree.add_plot(axes, showaxis=True)
mesh = self.tritree.to_conformmesh(options)
fig = pl.figure()
axes = a3.Axes3D(fig)
mesh.add_plot(axes, showaxis=True)
space = SurfaceLagrangeFiniteElementSpace(mesh,
self.surface,
p=p,
scale=self.scale)
mesh0 = space.mesh
fig = pl.figure()
axes = a3.Axes3D(fig)
mesh0.add_plot(axes, showaxis=True)
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)
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, showaxis=True)
plt.show()
m = int(sys.argv[1])
p = int(sys.argv[2])
q = int(sys.argv[3])
if m == 1:
pde = SphereSinSinSinData()
mesh = pde.init_mesh()
elif m == 2:
model = ToruSurfacesData()
surface = model.surface
mesh = surface.init_mesh()
elif m == 3:
model = ElipsoidSurfaceData()
surface = model.surface
mesh = surface.init_mesh()
elif m == 4:
model = HeartSurfacetData()
surface = model.surface
mesh = surface.init_mesh()
maxit = 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)
for i in range(maxit):
fem = SurfacePoissonFEMModel(mesh, pde, p, q)
fem.solve()
Ndof[i] = len(fem.uh)