def interpolation(self, n=2, plot=True):
from fealpy.pde.poisson_2d import CosCosData
from fealpy.functionspace import ConformingVirtualElementSpace2d
pde = CosCosData()
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float64)
cell = np.array([(0, 1, 2, 3)], dtype=np.int_)
mesh = QuadrangleMesh(node, cell)
#mesh = PolygonMesh.from_mesh(mesh)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.uniform_refine(n=n)
#mesh.print()
space = ConformingVirtualElementSpace2d(mesh, p=1)
uI = space.interpolation(pde.solution)
up = space.project_to_smspace(uI)
error = space.integralalg.L2_error(pde.solution, up)
print(error)
if plot:
fig = plt.figure()
axes = fig.gca()
#mesh.add_halfedge_plot(axes, showindex=True)
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 coarsen_tri(self, maxit=2, method='rg', plot=True, rb=True):
cell = np.array([[0, 1, 2], [0, 2, 3], [1, 4, 5], [2, 1, 5]],
dtype=np.int)
node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]],
dtype=np.float)
if True:
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
isMarkedCell = np.array([0, 1, 0, 0, 1], dtype=np.bool_)
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
mesh.hedgecolor = color
mesh.refine_triangle_rg(isMarkedCell)
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
if 0:
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)
plt.show()
if method == 'rg':
if 1:
NC = mesh.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[[1, 2, 5, 6, 7, 9]] = True
print('*************lll*********')
mesh.coarsen_triangle_rg(isMarkedCell)
if 1:
NC = mesh.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[[0, 1, 2, 3, 4, 5, 6, 7]] = True
print('*************lll*********')
mesh.coarsen_triangle_rg(isMarkedCell)
NC = mesh.number_of_all_cells()
isMarkedCell = np.ones(NC, dtype=np.bool_)
print('*************lll*********')
mesh.refine_triangle_rg(isMarkedCell)
else:
color[[2, 3, 10, 11]] = 1
mesh.hedgecolor = color
isMarkedCell = np.array([0, 1, 1, 0, 0], dtype=np.bool_)
#isMarkedCell = np.array([0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ,0],
# dtype=np.bool_)
mesh.refine_triangle_nvb(isMarkedCell)
mesh.print()
if plot:
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)
plt.show()
def coarsen_quad(self, plot=True):
cell = np.array([[0, 1, 2, 3], [1, 4, 5, 2]], dtype=np.int)
node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]],
dtype=np.float)
mesh = QuadrangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
halfedge = mesh.ds.halfedge
NE = mesh.ds.NE
color = 3 * np.ones(NE * 2, dtype=np.int_)
color[1] = 1
while (color == 3).any():
red = color == 1
gre = color == 0
color[halfedge[red][:, [2, 3, 4]]] = 0
color[halfedge[gre][:, [2, 3, 4]]] = 1
colorlevel = ((color == 1) | (color == 2)).astype(np.int_)
mesh.hedgecolor = {'color': color, 'level': colorlevel}
for i in range(2):
NC = mesh.number_of_all_cells()
isMarkedCell = np.ones(NC, dtype=np.bool_)
mesh.refine_quad(isMarkedCell)
NC = mesh.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[[
1, 3, 12, 18, 20, 17, 16, 9, 7, 2, 4, 6, 7, 8, 9, 27, 15, 8, 23,
32, 5, 24, 16, 29, 4, 7, 28, 11, 14, 22, 31, 19
]] = True
mesh.coarsen_quad(isMarkedCell)
if 1:
NC = mesh.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[[
20, 21, 23, 22, 18, 24, 26, 11, 1, 7, 13, 3, 8, 15, 12, 17
]] = True
mesh.coarsen_quad(isMarkedCell)
for i in range(2):
print(i, '*************************************************')
NC = mesh.number_of_all_cells()
isMarkedCell = np.ones(NC, dtype=np.bool_)
mesh.refine_quad(isMarkedCell)
print(np.where(mesh.hedgecolor['color'] == 2))
print(np.c_[np.arange(mesh.ds.NE * 2), mesh.hedgecolor['color'],
mesh.hedgecolor['level']])
print(np.c_[np.arange(mesh.ds.NE * 2), mesh.halfedgedata['level']])
if plot:
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)
plt.show()
def refine_quad(self, l, plot=True):
cell = np.array([[0, 1, 2, 3], [1, 4, 5, 2]], dtype=np.int)
node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]],
dtype=np.float)
mesh = QuadrangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
halfedge = mesh.ds.halfedge
NE = mesh.ds.NE
color = 3 * np.ones(NE * 2, dtype=np.int_)
color[1] = 1
while (color == 3).any():
red = color == 1
gre = color == 0
color[halfedge[red][:, [2, 3, 4]]] = 0
color[halfedge[gre][:, [2, 3, 4]]] = 1
colorlevel = ((color == 1) | (color == 2)).astype(np.int_)
mesh.hedgecolor = {'color': color, 'level': colorlevel}
c = np.array([1, 10000.5])
r = 10000
h = 1e-2
k = 0
NB = 0
while k < l:
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_quad(markedcell1.astype(np.bool_))
k += 1
print('循环', k, '次***************************')
print(np.c_[np.arange(mesh.ds.NE * 2), mesh.hedgecolor['color'],
mesh.hedgecolor['level']])
if plot:
plt.close()
fig = plt.figure()
axes = fig.gca()
nindex = mesh.nodedata['level']
mesh.add_plot(axes)
#mesh.add_halfedge_plot(axes, showindex=True)
#mesh.find_node(axes, showindex=True, multiindex=nindex)
plt.show()
def data_structure(self, plot=True):
node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]],
dtype=np.float)
cell = np.array([[0, 1, 2], [0, 2, 3], [1, 4, 5], [2, 1, 5]],
dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.print()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def tri_cut_graph(self, fname, weight=None):
data = sio.loadmat(fname)
node = np.array(data['node'], dtype=np.float64)
cell = np.array(data['elem'] - 1, dtype=np.int_)
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh, closed=True)
mesh.ds.NV = 3
gamma = mesh.tri_cut_graph(weight=weight)
writer = MeshWriter(mesh)
writer.write(fname='test.vtu')
for i, index in enumerate(gamma):
writer = MeshWriter(mesh, etype='edge', index=index)
writer.write(fname='test' + str(i) + '.vtu')
def refine_halfedge(self, plot=True):
node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]],
dtype=np.float)
cell = np.array([[0, 1, 2], [0, 2, 3], [1, 4, 5], [2, 1, 5]],
dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
isMarkedCell = np.array([0, 1, 0, 0, 0], dtype=np.bool_)
isMarkedHEdge = mesh.mark_halfedge(isMarkedCell)
mesh.refine_halfedge(isMarkedHEdge)
mesh.print()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
#mesh.find_cell(axes, showindex=True)
plt.show()
def coarsen_poly(self, plot=True):
node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]],
dtype=np.float)
cell = np.array([[0, 1, 2], [0, 2, 3], [1, 4, 5], [2, 1, 5]],
dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
isMarkedCell = np.array([0, 0, 0, 1, 0], dtype=np.bool_)
mesh.refine_poly(isMarkedCell)
isMarkedCell = np.array([0, 0, 0, 0, 1, 1, 1], dtype=np.bool_)
mesh.coarsen_poly(isMarkedCell)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(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.init_level_info()
mesh.convexity()
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_tri(self, maxit=2, method='rg', plot=True, rb=True):
cell = np.array([[0, 1, 2], [0, 2, 3], [1, 4, 5], [2, 1, 5]],
dtype=np.int)
node = np.array([[0, 0], [1, 0], [1, 1], [0, 1], [2, 0], [2, 1]],
dtype=np.float)
if False:
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh.from_mesh(mesh)
mesh.ds.cell2hedge = np.array([0, 3, 2, 11, 10])
isMarkedCell = np.array([0, 1, 0, 0, 1], dtype=np.bool_)
#mesh.refine_triangle_rbg(isMarkedCell)
mesh.ds.NV = 3
cell = mesh.ds.cell_to_node()
node = mesh.entity('node')
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
if False:
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)
plt.show()
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
if method == 'rg':
color[[4, 13, 17, 28]] = 1
color[[23, 27]] = 2
color[[22, 26]] = 3
mesh.hedgecolor = color
isMarkedCell = np.array(
[0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], dtype=np.bool_)
mesh.refine_triangle_rg(isMarkedCell)
else:
color[[2, 3, 10, 11]] = 1
mesh.hedgecolor = color
isMarkedCell = np.array([0, 1, 1, 0, 0], dtype=np.bool_)
#isMarkedCell = np.array([0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ,0],
# dtype=np.bool_)
mesh.refine_triangle_nvb(isMarkedCell)
mesh.print()
if plot:
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)
plt.show()
if True:
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
if method == 'nvb':
color[[2, 3, 10, 11]] = 1
mesh.hedgecolor = color
c = np.array([0.8, 0.8])
r = 0.9
h = 1e-2
k = 0
NB = 0
start = time.time()
while k < maxit:
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
if method == 'rg':
mesh.refine_triangle_rg(markedcell1.astype(np.bool_))
else:
mesh.refine_triangle_nvb(markedcell1.astype(np.bool_))
k += 1
print('循环', k, '次***************************')
end = time.time()
print('用时', end - start)
if plot:
fig = plt.figure()
axes = fig.gca()
nindex = mesh.nodedata['level']
mesh.add_plot(axes)
#mesh.add_halfedge_plot(axes, showindex=True)
#mesh.find_node(axes, showindex=True, multiindex=nindex)
#mesh.find_cell(axes, showindex=True)
#print(np.c_[np.arange(len(mesh.hedgecolor)), mesh.hedgecolor])
plt.show()
def adaptive_poly(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 = HalfEdgeMesh2d.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 = [1, 0, 0, 0, 2]
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()
"""
coarsened mesh
"""
#eta = [0,0,0,0,0,0,0,-1,0,-1,0,-1,0,-1]
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.add_halfedge_plot(axes, showindex=True)
#mesh.find_node(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.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(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