def project_test(self, u, p=2, mtype=0, plot=True):
from fealpy.mesh.simple_mesh_generator import triangle
if mtype == 0:
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)
elif mtype == 1:
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
dtype=np.float)
cell = np.array([0, 1, 2, 3, 0, 2], dtype=np.int)
cellLocation = np.array([0, 3, 6], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
elif mtype == 2:
h = 0.025
mesh = triangle([-1, 1, -1, 1], h, meshtype='polygon')
elif mtype == 3:
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
dtype=np.float)
cell = np.array([[0, 1, 2, 3]], dtype=np.int)
mesh = QuadrangleMesh(node, cell)
mesh.uniform_refine()
mesh = PolygonMesh.from_mesh(mesh)
elif mtype == 4:
node = np.array([(-1, -1), (1, -1), (1, 0), (1, 1), (-1, 1),
(-1, 0)],
dtype=np.float)
cell = np.array([0, 1, 2, 5, 2, 3, 4, 5], dtype=np.int)
cellLocation = np.array([0, 4, 8], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
if True:
cell, cellLocation = mesh.entity('cell')
edge = mesh.entity('edge')
cell2edge = mesh.ds.cell_to_edge()
bc = mesh.entity_barycenter('edge')
uspace = ReducedDivFreeNonConformingVirtualElementSpace2d(mesh, p)
up = uspace.project(u)
up = uspace.project_to_smspace(up)
print(up)
integralalg = uspace.integralalg
error = integralalg.L2_error(u, up)
print(error)
A = uspace.matrix_A()
P = uspace.matrix_P()
sio.savemat('A.mat', {"A": A.toarray(), "P": P.toarray()})
if plot:
mesh.print()
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_edge(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def cell_to_node(self):
node = np.array([(0.0, 0.0), (0.0, 1.0), (0.0, 2.0), (1.0, 0.0),
(1.0, 1.0), (1.0, 2.0), (2.0, 0.0), (2.0, 1.0),
(2.0, 2.0)],
dtype=np.float)
cell = np.array([0, 3, 4, 4, 1, 0, 1, 4, 5, 2, 3, 6, 7, 4, 4, 7, 8, 5],
dtype=np.int)
cellLocation = np.array([0, 3, 6, 10, 14, 18], dtype=np.int)
print('node:', node)
print('cell:', cell)
print('cellLocation:', cellLocation)
mesh = PolygonMesh(node, cell, cellLocation)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.print()
cell, cellLocation = mesh.entity('cell')
print('cell:', cell)
print('cellLocation:', cellLocation)
plt.show()
def edge_to_cell_test(self, plot=True):
node = np.array([(0.0, 0.0), (0.0, 1.0), (0.0, 2.0), (1.0, 0.0),
(1.0, 1.0), (1.0, 2.0), (2.0, 0.0), (2.0, 1.0),
(2.0, 2.0)],
dtype=np.float)
cell = np.array([0, 3, 4, 4, 1, 0, 1, 4, 5, 2, 3, 6, 7, 4, 4, 7, 8, 5],
dtype=np.int)
cellLocation = np.array([0, 3, 6, 10, 14, 18], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
mesh = HalfEdgePolygonMesh.from_polygonmesh(mesh)
NE = mesh.number_of_edges()
edge = mesh.entity('edge')
edge2cell = mesh.ds.edge_to_cell()
print('edge:')
for i in range(NE):
print(i, ":", edge[i], edge2cell[i])
NC = mesh.number_of_cells()
cell, cellLocation = mesh.entity('cell')
cell2edge = mesh.ds.cell_to_edge()
for i in range(NC):
print(i, ":", cell[cellLocation[i]:cellLocation[i + 1]])
print(i, ":", cell2edge[cellLocation[i]:cellLocation[i + 1]])
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_edge(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def boundary_edge_to_edge_test(self, plot=True):
node = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0)],
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)
mesh.ds.boundary_edge_to_edge()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_edge(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def project_test(self, u, p=2, mtype=0, plot=True):
from fealpy.mesh.simple_mesh_generator import triangle
if mtype == 0:
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)
elif mtype == 1:
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
dtype=np.float)
cell = np.array([0, 1, 2, 3, 0, 2], dtype=np.int)
cellLocation = np.array([0, 3, 6], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
elif mtype == 2:
h = 0.1
mesh = triangle([-1, 1, -1, 1], h, meshtype='polygon')
elif mtype == 3:
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
dtype=np.float)
cell = np.array([[0, 1, 2, 3]], dtype=np.int)
mesh = QuadrangleMesh(node, cell)
mesh.uniform_refine()
mesh = PolygonMesh.from_mesh(mesh)
cell, cellLocation = mesh.entity('cell')
edge = mesh.entity('edge')
cell2edge = mesh.ds.cell_to_edge()
uspace = DivFreeNonConformingVirtualElementSpace2d(mesh, p)
up = uspace.project(u)
print(up)
up = uspace.project_to_smspace(up)
print(up)
integralalg = uspace.integralalg
error = integralalg.L2_error(u, up)
print(error)
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_edge(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def convexity(self):
node = np.array([[0, 0], [2, 0], [2, 1], [1, 1], [1, 2], [1, 3],
[1, 4], [2, 4], [2, 5], [0, 5], [0, 2]],
dtype=np.float)
cell = np.array([0, 1, 2, 3, 4, 10, 5, 6, 7, 8, 9, 10, 4],
dtype=np.int_)
cellLocation = np.array([0, 6, 13], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.print()
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
mesh.add_halfedge_plot(axes, showindex=True)
plt.show()
def refine_test(self, plot=True):
node = np.array([(0.0, 0.0), (0.0, 1.0), (0.0, 2.0), (1.0, 0.0),
(1.0, 1.0), (1.0, 2.0), (2.0, 0.0), (2.0, 1.0),
(2.0, 2.0)],
dtype=np.float)
cell = np.array([0, 3, 4, 4, 1, 0, 1, 4, 5, 2, 3, 6, 7, 4, 4, 7, 8, 5],
dtype=np.int)
cellLocation = np.array([0, 3, 6, 10, 14, 18], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
mesh = HalfEdgePolygonMesh.from_polygonmesh(mesh)
isMarkedCell = np.zeros(5, dtype=np.bool)
isMarkedCell[-1] = True
isMarkedCell[-2] = True
mesh.refine(isMarkedCell)
if True:
NC = mesh.number_of_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool)
isMarkedCell[2] = True
mesh.refine(isMarkedCell)
if True:
NC = mesh.number_of_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool)
isMarkedCell[1] = True
mesh.refine(isMarkedCell)
if True:
NC = mesh.number_of_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool)
isMarkedCell[13] = True
mesh.refine(isMarkedCell)
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_edge(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def from_polygonmesh_test(self, plot=True):
node = np.array([(0.0, 0.0), (0.0, 1.0), (0.0, 2.0), (1.0, 0.0),
(1.0, 1.0), (1.0, 2.0), (2.0, 0.0), (2.0, 1.0),
(2.0, 2.0)],
dtype=np.float)
cell = np.array([0, 3, 4, 4, 1, 0, 1, 4, 5, 2, 3, 6, 7, 4, 4, 7, 8, 5],
dtype=np.int)
cellLocation = np.array([0, 3, 6, 10, 14, 18], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
a = mesh.entity_measure('cell')
mesh = HalfEdgePolygonMesh.from_polygonmesh(mesh)
a = mesh.entity_measure('cell')
mesh.print()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_edge(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def refine_with_flag_test(self, plot=True):
node = np.array([(0.0, 0.0), (0.0, 1.0), (0.0, 2.0), (1.0, 0.0),
(1.0, 1.0), (1.0, 2.0), (2.0, 0.0), (2.0, 1.0),
(2.0, 2.0)],
dtype=np.float)
cell = np.array([0, 3, 4, 4, 1, 0, 1, 4, 5, 2, 3, 6, 7, 4, 4, 7, 8, 5],
dtype=np.int)
cellLocation = np.array([0, 3, 6, 10, 14, 18], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
mesh = HalfEdgePolygonMesh.from_polygonmesh(mesh)
NE = mesh.number_of_edges()
NC = mesh.number_of_cells()
name = 'rflag'
val = np.zeros(2 * NE, dtype=np.int)
mesh.set_data(name, val, 'halfedge')
isMarkedCell = np.zeros(NC + 1, dtype=np.bool)
isMarkedCell[2] = True
mesh.refine_with_flag(isMarkedCell, rflag=name, dflag=False)
NC = mesh.number_of_cells()
isMarkedCell = np.zeros(NC + 1, dtype=np.bool)
isMarkedCell[6] = True
mesh.refine_with_flag(isMarkedCell, rflag=name, dflag=False)
if True:
NC = mesh.number_of_cells()
isMarkedCell = np.zeros(NC + 1, dtype=np.bool)
isMarkedCell[3] = True
mesh.refine_with_flag(isMarkedCell, rflag=name, dflag=False)
if True:
NC = mesh.number_of_cells()
isMarkedCell = np.zeros(NC + 1, dtype=np.bool)
isMarkedCell[1] = True
mesh.refine_with_flag(isMarkedCell, rflag=name, dflag=False)
if True:
NC = mesh.number_of_cells()
isMarkedCell = np.zeros(NC + 1, dtype=np.bool)
isMarkedCell[5] = True
isMarkedCell[13] = True
mesh.refine_with_flag(isMarkedCell, rflag=name, dflag=False)
if True:
NC = mesh.number_of_cells()
isMarkedCell = np.zeros(NC + 1, dtype=np.bool)
isMarkedCell[0] = True
isMarkedCell[1] = True
mesh.refine_with_flag(isMarkedCell, rflag=name, dflag=False)
print("rflag:\n")
for i, val in enumerate(mesh.halfedgedata[name]):
print(i, ':', val, mesh.ds.halfedge[i, 0:2])
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
#mesh.find_edge(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
node = np.array([ (0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float)
cell = np.array([0, 1, 2, 3], dtype=np.int)
cellLocation = np.array([0, 4], dtype=np.int)
pmesh = PolygonMesh(node, cell, cellLocation)
space = VectorScaledMonomialSpace2d(pmesh, p)
phi = space.basis(point)
print('phi', phi)
gphi = space.grad_basis(point)
print('gphi', gphi)
dphi = space.div_basis(point)
print('dphi', dphi)
gdphi = space.grad_div_basis(point)
print('gdphi', gdphi)
sphi = space.strain_basis(point)
print('sphi', sphi)
dsphi = space.div_strain_basis(point)
print('dsphi', dsphi)
fig = plt.figure()
axes = fig.gca()
pmesh.add_plot(axes)
pmesh.find_node(axes, showindex=True)
pmesh.find_edge(axes, showindex=True)
pmesh.find_cell(axes, showindex=True)
plt.show()
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)
qf = mesh.integrator(7)
space = NonConformingVirtualElementSpace2d(mesh, p=2)
print("Cell2dof:\n", space.cell_to_dof())
print("Interpolation points:\n", space.interpolation_points())
print("H:\n", space.H)
print("D:\n", space.D)
print("G:\n", space.G)
print("B:\n", space.B)
integralalg = PolygonMeshIntegralAlg(qf,
mesh,
barycenter=space.smspace.barycenter)
G = space.matrix_G_test(integralalg)
print("G:\n", G)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_node(axes,
node=space.interpolation_points(),
showindex=True,
color='b')
plt.show()
def adaptive_poly_test(self, plot=True):
""""
initial mesh
"""
node = np.array([(0.0, 0.0), (0.0, 1.0), (0.0, 2.0), (1.0, 0.0),
(1.0, 1.0), (1.0, 2.0), (2.0, 0.0), (2.0, 1.0),
(2.0, 2.0)],
dtype=np.float)
cell = np.array([0, 3, 4, 4, 1, 0, 1, 4, 5, 2, 3, 6, 7, 4, 4, 7, 8, 5],
dtype=np.int)
cellLocation = np.array([0, 3, 6, 10, 14, 18], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
mesh = HalfEdgeMesh.from_mesh(mesh)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
NE = mesh.number_of_edges()
nC = mesh.number_of_cells()
"""
refined mesh
"""
aopts = mesh.adaptive_options(method='numrefine',
maxcoarsen=3,
HB=True)
eta = [0, 0, 1, 1, 1]
mesh.adaptive(eta, aopts)
print('r', aopts['HB'])
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
mesh.from_mesh(mesh)
"""
coarsened mesh
"""
eta = [0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1]
#eta = [0,0,0,0,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2]
mesh.adaptive(eta, aopts)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
NAC = mesh.number_of_all_cells() # 包括外部区域和洞
cindex = range(mesh.ds.cellstart, NAC)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True, multiindex=cindex)
NN = mesh.number_of_nodes()
nindex = np.zeros(NN, dtype=np.int)
halfedge = mesh.ds.halfedge
nindex[halfedge[:, 0]] = mesh.get_data('halfedge', 'level')
cindex = mesh.get_data('cell', 'level')
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True, multiindex=nindex)
mesh.find_cell(axes, showindex=True, multiindex=cindex)
plt.show()
else:
return mesh
def two_cell_test(self, p=2, plot=True):
from fealpy.pde.stokes_model_2d import StokesModelData_7
pde = StokesModelData_7()
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1), (3, -1), (3, 1)],
dtype=np.float)
cell = np.array([0, 1, 2, 3, 1, 4, 5, 2], dtype=np.int)
cellLocation = np.array([0, 4, 8], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
uspace = DivFreeNonConformingVirtualElementSpace2d(mesh, p)
cell2dof = uspace.cell_to_dof()
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)
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_edge(axes, showindex=True)
plt.show()
def refine_poly(self, plot=True):
node = np.array([(0.0, 0.0), (0.0, 1.0), (0.0, 2.0), (1.0, 0.0),
(1.0, 1.0), (1.0, 2.0), (2.0, 0.0), (2.0, 1.0),
(2.0, 2.0)],
dtype=np.float)
cell = np.array([0, 3, 4, 4, 1, 0, 1, 4, 5, 2, 3, 6, 7, 4, 4, 7, 8, 5],
dtype=np.int)
cellLocation = np.array([0, 3, 6, 10, 14, 18], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
if False:
NC = mesh.ds.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[:] = True
mesh.refine_poly(isMarkedCell)
NC = mesh.ds.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[[1, 2, 3, 4, 7, 10]] = True
i = 0
mesh.refine_poly(isMarkedCell)
NC = mesh.ds.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[[17, 19, 36, 24, 14, 21, 34]] = True
i = 1
mesh.refine_poly(isMarkedCell)
NC = mesh.ds.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[[14, 16]] = True
i = 1
mesh.refine_poly(isMarkedCell)
if True:
c = np.array([1, 1])
r = 0.8
h = 1e-2
k = 0
NB = 0
while k < 8:
halfedge = mesh.ds.halfedge
halfedge1 = halfedge[:, 3]
node = mesh.node
flag = node - c
flag = flag[:, 0]**2 + flag[:, 1]**2
flag = flag <= r**2
flag1 = flag[halfedge[:, 0]].astype(int)
flag2 = flag[halfedge[halfedge1, 0]].astype(int)
markedge = flag1 + flag2 == 1
markedcell = halfedge[markedge, 1]
markedcell = np.unique(markedcell)
cell = np.unique(halfedge[:, 1])
nc = cell.shape[0]
markedcell1 = np.zeros(nc)
markedcell1[markedcell] = 1
print('makee', markedcell)
mesh.refine_poly(markedcell1.astype(np.bool_))
k += 1
print('循环', k, '次***************************')
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
#mesh.find_cell(axes, showindex=True)
#mesh.add_halfedge_plot(axes, showindex=True)
plt.show()
def stokes_equation_test(self, p=2, maxit=4, mtype=1):
from scipy.sparse import bmat
from fealpy.pde.Stokes_Model_2d import CosSinData, PolyY2X2Data
from fealpy.mesh.simple_mesh_generator import triangle
h = 0.4
#pde = CosSinData()
pde = PolyY2X2Data()
error = np.zeros((maxit, ), dtype=np.float)
for i in range(maxit):
if mtype == 0:
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)
else:
mesh = pde.init_mesh(n=i + 2, meshtype='poly')
NE = mesh.number_of_edges()
NC = mesh.number_of_cells()
idof = (p - 2) * (p - 1) // 2
if True:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
uspace = ReducedDivFreeNonConformingVirtualElementSpace2d(mesh, p)
pspace = ScaledMonomialSpace2d(mesh, 0)
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()
F = uspace.source_vector(pde.source)
AA = bmat([[A, P.T], [P, None]], format='csr')
FF = np.block([F, np.zeros(pdof, dtype=uspace.ftype)])
x = np.block([uh, ph])
isBdDof = np.block(
[isBdDof, isBdDof,
np.zeros(NC * idof + pdof, dtype=np.bool)])
gdof = udof + pdof
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:]
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:])
plt.show()
def refine_poly(self, plot=True):
node = np.array([(0.0, 0.0), (0.0, 1.0), (0.0, 2.0), (1.0, 0.0),
(1.0, 1.0), (1.0, 2.0), (2.0, 0.0), (2.0, 1.0),
(2.0, 2.0)],
dtype=np.float)
cell = np.array([0, 3, 4, 4, 1, 0, 1, 4, 5, 2, 3, 6, 7, 4, 4, 7, 8, 5],
dtype=np.int)
cellLocation = np.array([0, 3, 6, 10, 14, 18], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.uniform_refine(n=2)
print(mesh.number_of_nodes())
#fig = plt.figure()
#axes = fig.gca()
#mesh.add_plot(axes)
#mesh.find_node(axes, showindex=True)
#mesh.find_cell(axes, showindex=True)
NE = mesh.number_of_edges()
NC = mesh.number_of_cells()
if True:
isMarkedCell = mesh.mark_helper([2])
mesh.refine_poly(isMarkedCell)
if False:
isMarkedCell = mesh.mark_helper([6])
mesh.refine_poly(isMarkedCell, dflag=False)
if False:
isMarkedCell = mesh.mark_helper([3])
mesh.refine_poly(isMarkedCell, dflag=False)
if False:
isMarkedCell = mesh.mark_helper([1, 5])
mesh.refine_poly(isMarkedCell)
if False:
isMarkedCell = mesh.mark_helper([1, 12])
mesh.refine_poly(isMarkedCell, dflag=False)
if False:
isMarkedCell = mesh.mark_helper([0, 21])
mesh.refine_poly(isMarkedCell, dflag=False)
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
if 0:
NAC = mesh.number_of_all_cells() # 包括外部区域和洞
cindex = range(mesh.ds.cellstart, NAC)
fig = plt.figure()
axes = fig.gca()
#mesh.add_plot(axes)
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True, multiindex=cindex)
NN = mesh.number_of_nodes()
nindex = np.zeros(NN, dtype=np.int)
halfedge = mesh.ds.halfedge
nindex[halfedge[:, 0]] = mesh.get_data('halfedge', 'level')
cindex = mesh.get_data('cell', 'level')
fig = plt.figure()
axes = fig.gca()
#mesh.add_plot(axes)
mesh.find_node(axes, showindex=True, multiindex=nindex)
#mesh.find_cell(axes, showindex=True, multiindex=cindex)
plt.show()
else:
return mesh
def refine_poly_test(self, plot=True):
node = np.array([(0.0, 0.0), (0.0, 1.0), (0.0, 2.0), (1.0, 0.0),
(1.0, 1.0), (1.0, 2.0), (2.0, 0.0), (2.0, 1.0),
(2.0, 2.0)],
dtype=np.float)
cell = np.array([0, 3, 4, 4, 1, 0, 1, 4, 5, 2, 3, 6, 7, 4, 4, 7, 8, 5],
dtype=np.int)
cellLocation = np.array([0, 3, 6, 10, 14, 18], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
mesh = HalfEdgeMesh.from_mesh(mesh)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
clevel = mesh.celldata['level']
print(clevel)
NE = mesh.number_of_edges()
NC = mesh.number_of_cells()
if True:
isMarkedCell = mesh.mark_helper([2])
mesh.refine_poly(isMarkedCell, dflag=False)
if False:
isMarkedCell = mesh.mark_helper([6])
mesh.refine_poly(isMarkedCell, dflag=False)
if False:
isMarkedCell = mesh.mark_helper([3])
mesh.refine_poly(isMarkedCell, dflag=False)
if 1:
isMarkedCell = mesh.mark_helper([1, 5])
mesh.refine_poly(isMarkedCell, dflag=False)
if False:
isMarkedCell = mesh.mark_helper([1, 12])
mesh.refine_poly(isMarkedCell, dflag=False)
if False:
isMarkedCell = mesh.mark_helper([0, 21])
mesh.refine_poly(isMarkedCell, dflag=False)
clevel = mesh.celldata['level']
print(clevel)
#print("halfedge level:\n")
#for i, val in enumerate(mesh.halfedgedata['level']):
# print(i, ':', val, mesh.ds.halfedge[i, 0:2])
#print("cell level:\n")
#for i, val in enumerate(mesh.celldata['level']):
# print(i, ':', val)
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
NAC = mesh.number_of_all_cells() # 包括外部区域和洞
cindex = range(mesh.ds.cellstart, NAC)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_cell(axes, showindex=True, multiindex=cindex)
NN = mesh.number_of_nodes()
nindex = np.zeros(NN, dtype=np.int)
halfedge = mesh.ds.halfedge
nindex[halfedge[:, 0]] = mesh.get_data('halfedge', 'level')
cindex = mesh.get_data('cell', 'level')
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True, multiindex=nindex)
mesh.find_cell(axes, showindex=True, multiindex=cindex)
plt.show()
else:
return mesh
import numpy as np
import matplotlib.pyplot as plt
from fealpy.mesh import PolygonMesh, HalfEdgeMesh2d
node3 = np.array([(0.0, 0.0), (0.0, 1.0), (0.0, 2.0), (1.0, 0.0), (1.0, 1.0),
(1.0, 2.0), (2.0, 0.0), (2.0, 1.0), (2.0, 2.0)],
dtype=np.float64)
cell3 = np.array([0, 3, 4, 4, 1, 0, 1, 4, 5, 2, 3, 6, 7, 4, 4, 7, 8, 5],
dtype=np.int)
cellLocation = np.array([0, 3, 6, 10, 14, 18], dtype=np.int)
mesh3 = PolygonMesh(node3, cell3, cellLocation)
mesh3 = HalfEdgeMesh2d.from_mesh(mesh3)
mesh3.uniform_refine(2) # 这里一致加密的时候会报错
node3 = mesh3.entity("node")
edge3 = mesh3.entity("edge")
cell3, cellLocation = mesh3.entity("cell")
halfedge = mesh3.entity("halfedge")
fig3 = plt.figure()
axes3 = fig3.gca()
mesh3.add_plot(axes3)
mesh3.find_node(axes3, showindex=True)
mesh3.find_edge(axes3)
plt.show()
