def stokes_equation_test(self, p=2, maxit=4):
from scipy.sparse import bmat
from fealpy.pde.stokes_model_2d import StokesModelData_7
from fealpy.mesh.simple_mesh_generator import triangle
h = 0.4
pde = StokesModelData_7()
error = np.zeros((maxit, ), dtype=np.float)
for i in range(maxit):
mesh = pde.init_mesh(n=i + 2, meshtype='poly')
if 0:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
plt.show()
uspace = DivFreeNonConformingVirtualElementSpace2d(mesh, p)
pspace = ScaledMonomialSpace2d(mesh, p - 1)
ldof = pspace.number_of_local_dofs()
isBdDof = uspace.boundary_dof()
udof = uspace.number_of_global_dofs()
pdof = pspace.number_of_global_dofs()
uh = uspace.function()
ph = pspace.function()
uspace.set_dirichlet_bc(uh, pde.dirichlet)
A = uspace.matrix_A()
P = uspace.matrix_P()
C = uspace.CM[:, 0, :ldof].reshape(-1)
F = uspace.source_vector(pde.source)
AA = bmat([[A, P.T, None], [P, None, C[:, None]], [None, C, None]],
format='csr')
FF = np.block([F, np.zeros(pdof + 1, dtype=uspace.ftype)])
x = np.block([uh, ph, np.zeros((1, ), dtype=uspace.ftype)])
isBdDof = np.r_['0', isBdDof, np.zeros(pdof + 1, dtype=np.bool)]
gdof = udof + pdof + 1
FF -= AA @ x
bdIdx = np.zeros(gdof, dtype=np.int)
bdIdx[isBdDof] = 1
Tbd = spdiags(bdIdx, 0, gdof, gdof)
T = spdiags(1 - bdIdx, 0, gdof, gdof)
AA = T @ AA @ T + Tbd
FF[isBdDof] = x[isBdDof]
x[:] = spsolve(AA, FF)
uh[:] = x[:udof]
ph[:] = x[udof:-1]
up = uspace.project_to_smspace(uh)
integralalg = uspace.integralalg
error[i] = integralalg.L2_error(pde.velocity, up)
h /= 2
print(error)
print(error[0:-1] / error[1:])
def one_cell_test_0(self, p=2):
from fealpy.pde.stokes_model_2d import StokesModelData_7
pde = StokesModelData_7()
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)], dtype=np.float)
cell = np.array([0, 1, 2, 3], dtype=np.int)
cellLocation = np.array([0, 4], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
uspace = DivFreeNonConformingVirtualElementSpace2d(mesh, p)
pspace = ScaledMonomialSpace2d(mesh, p - 1)
ldof = pspace.number_of_local_dofs()
isBdDof = uspace.boundary_dof()
udof = uspace.number_of_global_dofs()
pdof = pspace.number_of_global_dofs()
uh = uspace.function()
ph = pspace.function()
uspace.set_dirichlet_bc(uh, pde.dirichlet)
A = uspace.matrix_A()
P = uspace.matrix_P()
C = uspace.CM[:, 0, :ldof].reshape(-1)
F = uspace.source_vector(pde.source)
AA = bmat([[A, P.T, None], [P, None, C[:, None]], [None, C, None]],
format='csr')
FF = np.block([F, np.zeros(pdof + 1, dtype=uspace.ftype)])
x = np.block([uh, ph, np.zeros((1, ), dtype=uspace.ftype)])
isBdDof = np.r_['0', isBdDof, np.zeros(pdof + 1, dtype=np.bool)]
gdof = udof + pdof + 1
FF -= AA @ x
bdIdx = np.zeros(gdof, dtype=np.int)
bdIdx[isBdDof] = 1
Tbd = spdiags(bdIdx, 0, gdof, gdof)
T = spdiags(1 - bdIdx, 0, gdof, gdof)
AA = T @ AA @ T + Tbd
FF[isBdDof] = x[isBdDof]
x[:] = spsolve(AA, FF)
uh[:] = x[:udof]
ph[:] = x[udof:-1]
print('ph:', ph)
print('uh:', uh)
up = uspace.project_to_smspace(uh)
print('up:', up)
integralalg = uspace.integralalg
error = integralalg.L2_error(pde.velocity, up)
print(error)
uv = uspace.project(pde.velocity)
print('uproject:', uv)
up = uspace.project_to_smspace(uv)
print('up', up)
error = integralalg.L2_error(pde.velocity, up)
print(error)