def test_SurfaceParabolicFEMModel_time(self, maxit=2):
from fealpy.pde.surface_parabolic_model_3d import SinSinSinExpDataSphere
pde = SinSinSinExpDataSphere()
mesh = pde.init_mesh(n=5)
timeline = pde.time_mesh(0, 1, 2)
errorType = ['$||u-u_h||_0$']
error = np.zeros((len(errorType), maxit), dtype=mesh.ftype)
Ndof = np.zeros(maxit, dtype=mesh.itype)
for i in range(maxit):
print(i)
dmodel = SurfaceParabolicFEMModel(pde, mesh)
Ndof[i] = dmodel.space.number_of_global_dofs()
uh = dmodel.init_solution(timeline)
timeline.time_integration(uh, dmodel, self.solver.divide)
u = lambda x:dmodel.pde.solution(x, 1.0)
uh = dmodel.space.function(array=uh[:, -1])
error[0, i] = dmodel.space.integralalg.L2_error(u, uh)
# timeline.uniform_refine()
mesh.uniform_refine(surface=pde.surface)
show_error_table(Ndof, errorType, error)
showmultirate(plt, 0, Ndof, error, errorType)
plt.show()
def test_SurfaceParabolicFEMModel_sdc_time(self, maxit=4):
from fealpy.pde.surface_parabolic_model_3d import SinSinSinExpDataSphere
pde = SinSinSinExpDataSphere()
mesh = pde.init_mesh(n=5)
timeline = pde.time_mesh(0, 1, 2, timeline='chebyshev')
errorType = ['$|| u - u_h ||_\infty$', '$||u-u_h||_0$']
errorMatrix = np.zeros((len(errorType), maxit), dtype=mesh.ftype)
Ndof = np.zeros(maxit, dtype=mesh.itype)
for i in range(maxit):
print(i)
dmodel = SurfaceParabolicFEMModel(pde, mesh, p=1)
Ndof[i] = dmodel.space.number_of_global_dofs()
uh = dmodel.init_solution(timeline)
timeline.time_integration(uh, dmodel, self.solver.divide, nupdate=1)
uI = dmodel.interpolation(pde.solution, timeline)
errorMatrix[0, i] = np.max(np.abs(uI - uh))
u = lambda x:dmodel.pde.solution(x, 1.0)
uh = dmodel.space.function(array=uh[:, -1])
errorMatrix[1, i] = dmodel.space.integralalg.L2_error(u, uh)
print(errorMatrix)
timeline.uniform_refine()
mesh.uniform_refine(surface=pde.surface)
show_error_table(Ndof, errorType, errorMatrix)
showmultirate(plt, 0, Ndof, errorMatrix, errorType)
plt.show()
def my_show_error_table(N, errorType, errorMatrix, showTable='No'):
if showTable is 'No':
f = 'e'
pre = 4
sep = ' & '
out = sys.stdout
end = '\n'
s = 'Dof' + sep + np.array2string(N, separator=sep,
)
s = s.replace('\n', '')
s = s.replace('[', '')
s = s.replace(']', '')
print(s, file=out, end=end)
n = len(errorType)
ff = '%.' + str(pre) + f
for i in range(n):
first = errorType[i]
line = errorMatrix[i]
s = first + sep + np.array2string(line, separator=sep,
precision=pre, formatter=dict(float=lambda x: ff % x))
s = s.replace('\n', '')
s = s.replace('[', '')
s = s.replace(']', '')
print(s, file=out, end=end)
else:
show_error_table(N, errorType, errorMatrix)
def test_ParabolicFEMModel_time(self, maxit=4):
pde = CosCosExpData(0.1)
mesh = pde.init_mesh(n=0)
timeline = UniformTimeLine(0, 1, 2)
errorType = ['$|| u - u_h ||_\infty$', '$||u-u_h||_0$']
errorMatrix = np.zeros((len(errorType), maxit), dtype=mesh.ftype)
Ndof = np.zeros(maxit, dtype=mesh.itype)
for i in range(maxit):
print(i)
model = ParabolicFEMModel(pde, mesh, p=1)
Ndof[i] = model.space.number_of_global_dofs()
uh = model.init_solution(timeline)
timeline.time_integration(uh, model, spsolve)
uI = model.interpolation(pde.solution, timeline)
errorMatrix[0, i] = np.max(np.abs(uI - uh))
u = lambda x: model.pde.solution(x, 1.0)
uh = model.space.function(array=uh[:, -1])
errorMatrix[1, i] = model.space.integralalg.L2_error(u, uh)
print(errorMatrix)
timeline.uniform_refine()
mesh.uniform_refine(surface=pde.surface)
show_error_table(Ndof, errorType, errorMatrix)
showmultirate(plt, 0, Ndof, errorMatrix, errorType)
plt.show()
#h0 /= 2
#mesh = distmesh2d(fd, h0, bbox, pfix, meshtype='polygon')
n *= 2
mesh = rectangledomainmesh([-2, 2, -2, 2],
nx=n,
ny=n,
meshtype='polygon')
vem.reinit(mesh)
data['errorMatrix'] = errorMatrix
data['Ndof'] = Ndof
fo = 'uh{}.mat'.format(p)
sio.matlab.savemat(fo.format(i + 1), data)
mesh.add_plot(plt, cellcolor='w')
show_error_table(Ndof, errorType, errorMatrix)
#fig2 = plt.figure()
#fig2.set_facecolor('white')
#axes = fig2.gca(projection='3d')
#x = mesh.point[:, 0]
#y = mesh.point[:, 1]
#tri = quadtree.leaf_cell(celltype='tri')
#s = axes.plot_trisurf(x, y, tri, vem.uh[:len(x)], cmap=plt.cm.jet, lw=0.0)
#fig2.colorbar(s)
#
#fig3 = plt.figure()
#fig3.set_facecolor('white')
#axes = fig3.gca(projection='3d')
#s = axes.plot_trisurf(x, y, tri, vem.uI-vem.gI, cmap=plt.cm.jet, lw=0.0)
#fig3.colorbar(s)
e0, e1, e2, e3, e4 = fem.get_error()
eta0 = fem.grad_recover_estimate()
eta1 = fem.laplace_recover_estimate(etype=1)
e5 = np.sqrt(np.sum(eta0**2))
e6 = np.sqrt(np.sum(eta1**2))
errorMatrix[0, i] = e0
errorMatrix[1, i] = e1
errorMatrix[2, i] = e5
errorMatrix[3, i] = e2
errorMatrix[4, i] = e3
errorMatrix[5, i] = e4
errorMatrix[6, i] = e6
show_error_table(Ndof, errorType, errorMatrix, end='\\\\\\hline\n')
showmultirate(plt, 1, Ndof, errorMatrix, errorType)
n = 4
if meshtype == 1:
#mesh = meshzoo.regular(box, n=n)
pass
elif meshtype == 2:
mesh = meshzoo.rice_mesh(box, n=n)
elif meshtype == 3:
mesh = meshzoo.cross_mesh(box, n=n)
elif meshtype == 4:
mesh = meshzoo.fishbone(box, n=n)
elif meshtype == 5:
mesh = load_mat_mesh('../data/square' + str(2) + '.mat')
elif meshtype == 6:
# error analysis
errorType = [
'$\| u - \Pi^\\nabla u_h\|_0$', '$\|\\nabla u - \\nabla \Pi^\\nabla u_h\|$'
]
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
for i in range(maxit - 1):
S = vem.project_to_smspace(data[i])
errorMatrix[0, i] = vem.L2_error(S.value)
errorMatrix[1, i] = vem.H1_semi_error(S.grad_value)
solution['errorMatrix'] = errorMatrix
solution['Ndof'] = Ndof
f = 'solution.mat'
sio.matlab.savemat(f, solution)
print(Ndof)
print(errorMatrix)
show_error_table(Ndof[:-1], errorType, errorMatrix[:, :-1])
fig2 = plt.figure()
fig2.set_facecolor('white')
axes = fig2.gca(projection='3d')
x = qmesh.point[:, 0]
y = qmesh.point[:, 1]
cell = qmesh.ds.cell
tri = np.r_['0', cell[:, [1, 2, 0]], cell[:, [3, 0, 2]]]
s = axes.plot_trisurf(x, y, tri, vem.uh[:len(x)], cmap=plt.cm.jet, lw=0.0)
fig2.colorbar(s)
plt.show()
