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)
errorMatrix[0, i] = fem.get_l2_error()
errorMatrix[1, i] = fem.get_L2_error()
errorMatrix[2, i] = fem.get_H1_semi_error()
if i < maxit - 1:
mesh.uniform_refine(1, pde.surface)
print('Ndof:', Ndof)
print('error:', errorMatrix)
showmultirate(plt, 0, Ndof, errorMatrix, errorType)
plt.show()
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)
Ndof[i] = len(fem.uh)
errorMatrix[0, i] = fem.get_l2_error()
errorMatrix[1, i] = fem.get_L2_error()
errorMatrix[2, i] = fem.get_H1_semi_error()
if i < maxit - 1:
tmesh.refine(marker=AdaptiveMarker(eta, theta=theta))
pmesh = tmesh.to_conformmesh()
fig = pl.figure()
axes = a3.Axes3D(fig)
pmesh.add_plot(axes)
import mpl_toolkits.mplot3d as a3 import pylab as pl p = int(sys.argv[1]) theta = 0.2 integrator = TriangleQuadrature(6) ralg = FEMFunctionRecoveryAlg() pde = SphereSinSinSinData() mesh = pde.init_mesh(5) tmesh = Tritree(mesh.node, mesh.ds.cell, irule=1) pmesh = tmesh.to_conformmesh() fig0 = pl.figure() axes0 = a3.Axes3D(fig0) pmesh.add_plot(axes0) pl.show() fem = SurfacePoissonFEMModel(pmesh, pde, p, integrator) fem.solve() uh = fem.uh print(uh) rguh = ralg.harmonic_average(uh) eta = fem.recover_estimate(rguh) tmesh.refine(marker=AdaptiveMarker(eta, theta=theta)) pmesh = tmesh.to_conformmesh() fem = SurfacePoissonFEMModel(pmesh, pde, p, integrator) fem.solve() uh = fem.uh print(uh) fig1 = pl.figure() axes1 = a3.Axes3D(fig1) pmesh.add_plot(axes1) pl.show()