def complex_mesh(r, filename, n):
import meshio
mesh = meshio.read(filename)
node = mesh.points
node = node[:,0:2]*r
cell = mesh.cells
mesh.node = node
mesh.cell = cell
cell = cell['triangle']
isUsingNode = np.zeros(node.shape[0], dtype=np.bool)
isUsingNode[cell] = True
NN = isUsingNode.sum()
idxmap = np.zeros(node.shape[0], dtype=np.int32)
idxmap[isUsingNode] = range(NN)
cell = idxmap[cell]
node = node[isUsingNode]
#cell = cell[:,::-1]
mesh = TriangleMesh(node,cell)
nmesh = TriangleMeshWithInfinityNode(mesh)
ppoint, pcell, pcellLocation = nmesh.to_polygonmesh()
pmesh = PolygonMesh(ppoint, pcell, pcellLocation)
hmesh = HalfEdgeMesh2d.from_mesh(pmesh)
hmesh.init_level_info()
hmesh.convexity()
hmesh.uniform_refine(n=n)
mesh = PolygonMesh.from_halfedgemesh(hmesh)
return mesh
def uniform_boundary_meshing_test(self, plot=True):
vertices = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0)],
dtype=np.float)
facets = np.array([(0, 1), (1, 2), (2, 3), (3, 0)], dtype=np.int)
subdomain = np.array([(1, 0), (1, 0), (1, 0), (1, 0)], dtype=np.int)
dof = np.array([1, 1, 1, 1], dtype=np.bool)
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain)
uniform_boundary_mesh = CVTPMesher(mesh)
uniform_boundary_mesh.uniform_boundary_meshing(n=2)
bnode = uniform_boundary_mesh.bnode
vor = Voronoi(bnode)
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, color='k', showindex=True)
mesh.find_node(axes, node=bnode, showindex=True)
voronoi_plot_2d(vor, ax=axes)
'''
cs = [axes.add_artist( plt.Circle(x, r, facecolor='none',
edgecolor='r')) for x, r in zip(center, radius)]
'''
fig = plt.figure()
axes = fig.gca()
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
plt.show()
def quad_refine():
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)
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 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 run(self, estimator='mix'):
problem = self.problem
options = self.optoptions
model = problem['objective']
optalg = SteepestDescentAlg(problem, options)
x, f, g, diff = optalg.run(maxit=1)
while True:
mesh = problem['mesh']
hmesh = HalfEdgeMesh2d.from_mesh(mesh)
cell, cellLocation = hmesh.entity('cell')
print('2', cellLocation)
aopts = hmesh.adaptive_options(method='mean',
maxcoarsen=3,
HB=True)
print('NN', mesh.number_of_nodes())
mu = problem['x0']
if estimator == 'mix':
eta = model.mix_estimate(mu, w=1)
if estimator == 'grad':
eta = model.estimate(q)
aopts['data'] = {'mu': mu}
S0 = model.vemspace.project_to_smspace(aopts['data']['mu'][:, 0])
S1 = model.vemspace.project_to_smspace(aopts['data']['mu'][:, 1])
hmesh.adaptive(eta, aopts)
#fig = plt.figure()
#axes = fig.gca()
#hmesh.add_plot(axes)
#hmesh.find_cell(axes, showindex=True)
#plt.show()
cell, cellLocation = hmesh.entity('cell')
print('3', cellLocation)
mesh = PolygonMesh.from_halfedgemesh(hmesh)
model.reinit(mesh)
aopts['data']['mu'] = np.zeros((model.gdof, 2))
aopts['data']['mu'][:, 0] = model.vemspace.interpolation(
S0, aopts['HB'])
aopts['data']['mu'][:, 1] = model.vemspace.interpolation(
S1, aopts['HB'])
problem['x0'] = aopts['data']['mu']
optalg = SteepestDescentAlg(problem, options)
x, f, g, diff = optalg.run(maxit=1)
problem['mesh'] = mesh
problem['x0'] = x
problem['rho'] = model.rho
self.problem = problem
if diff < options['FunValDiff']:
if (np.max(problem['rho'][:, 0]) < 1) and (np.min(
problem['rho'][:, 0]) > 0):
break
pass
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 halfedgemesh(n=4, h=4):
"""
半边数据结构的网格
"""
node = np.array([(0, 0), (h, 0), (h, h), (0, h)], dtype=np.float64)
cell = np.array([(0, 1, 2, 3)], dtype=np.int_)
mesh = QuadrangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.uniform_refine(n)
return mesh
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 from_edges(self, plot=True):
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)], dtype=np.float)
edge = np.array([(0, 1), (1, 2), (2, 3), (3, 0)], dtype=np.int)
edge2subdomain = np.array([(1, 0), (1, 0), (1, 0), (1, 0)],
dtype=np.int)
mesh = HalfEdgeMesh2d.from_edges(node, edge, edge2subdomain)
mesh.print()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_halfedge_plot(axes, showindex=True)
plt.show()
def harmonic_map(self, fanme):
reader = CCGMeshReader(fname)
tmesh = reader.read()
mesh = HalfEdgeMesh2d.from_mesh(tmesh, NV=3)
mesh.nodedata['rgb'] = tmesh.nodedata['rgb']
cmesh = self.ccgalg.harmonic_map(mesh)
cmesh.nodedata['rgb'] = tmesh.nodedata['rgb']
writer = MeshWriter(mesh)
writer.write(fname='face3.vtu')
writer = MeshWriter(cmesh)
writer.write(fname='face2.vtu')
def tri_cut_graph(self, fname):
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 = self.ccgalg.tri_cut_graph(mesh)
writer = MeshWriter(mesh)
writer.write(fname='test0.vtu')
for i, index in enumerate(gamma):
writer = MeshWriter(mesh, etype='edge', index=index)
writer.write(fname='test' + str(i + 1) + '.vtu')
def halfedgemesh(h=4, n=4):
"""
半边数据结构的网格
"""
node = h * 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)
return mesh
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 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 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 square_domain(self, plot=True):
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)], dtype=np.float)
edge = np.array([(0, 1), (1, 2), (2, 3), (3, 0)], dtype=np.int)
edge2subdomain = np.array([(1, 0), (1, 0), (1, 0), (1, 0)],
dtype=np.int)
mesh = HalfEdgeMesh2d.from_edges(node, edge, edge2subdomain)
alg = TriAdvancingFrontAlg(mesh)
alg.run()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_halfedge_plot(axes, showindex=True)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes)
plt.show()
def square_domain(self, plot=True):
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)], dtype=np.float)
edge = np.array([(0, 1), (1, 2), (2, 3), (3, 0)], dtype=np.int)
edge2subdomain = np.array([(1, 0), (1, 0), (1, 0), (1, 0)],
dtype=np.int)
mesh = HalfEdgeMesh2d.from_edges(node, edge, edge2subdomain)
alg = TriAdvancingFrontAlg(mesh)
tri, fnode = alg.run()
node = mesh.entity('node')
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes)
node = np.r_['0', node, fnode]
fig = plt.figure()
axes = fig.gca()
axes.triplot(node[:, 0], node[:, 1], tri.simplices)
axes.set_axis_off()
axes.set_aspect('equal')
plt.show()
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()
def Lloyd_test(self, domain='square', plot=True):
if domain == 'square':
vertices = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0),
(0.0, 1.0)],
dtype=np.float)
facets = np.array([(0, 1), (1, 2), (2, 3), (3, 0)], dtype=np.int)
subdomain = np.array([(1, 0), (1, 0), (1, 0), (1, 0)],
dtype=np.int)
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain)
uniform_mesh = CVTPMesher(mesh)
uniform_mesh.uniform_meshing(refine=2)
elif domain == 'LShape':
vertices = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0),
(0.0, 1.0), (-1.0, 1.0), (-1.0, 0.0),
(-1.0, -1.0), (0.0, -1.0)],
dtype=np.float)
fixed = np.array([1, 1, 1, 0, 1, 0, 1, 1], dtype=np.bool)
facets = np.array([(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6),
(6, 7), (7, 0)],
dtype=np.int)
subdomain = np.array([
(1, 0),
(1, 0),
(1, 0),
(1, 0),
(1, 0),
(1, 0),
(1, 0),
(1, 0),
],
dtype=np.int)
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain,
fixed)
uniform_mesh = CVTPMesher(mesh)
uniform_mesh.uniform_meshing(refine=2)
elif domain == 'circle':
n = 20
h = 2 * np.pi / n
theta = np.arange(0, 2 * np.pi, h)
vertices = np.zeros((n, 2), dtype=np.float)
vertices[:, 0] = np.cos(theta)
vertices[:, 1] = np.sin(theta)
fixed = np.ones(n, dtype=np.bool)
facets = np.zeros((n, 2), dtype=np.int)
facets[:, 0] = range(0, n)
facets[:-1, 1] = range(1, n)
subdomain = np.zeros((n, 2), dtype=np.int)
subdomain[:, 0] = 1
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain,
fixed)
uniform_mesh = CVTPMesher(mesh)
uniform_mesh.uniform_meshing(refine=0)
elif domain == 'partition1':
vertices = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0),
(0.0, 1.0), (0.5, 0.5)],
dtype=np.float)
facets = np.array([(0, 1), (1, 2), (2, 3), (3, 0), (0, 4), (4, 3),
(4, 1), (4, 2)],
dtype=np.int)
subdomain = np.array([(1, 0), (2, 0), (3, 0), (4, 0), (4, 1),
(4, 3), (2, 1), (3, 2)],
dtype=np.int)
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain)
uniform_mesh = CVTPMesher(mesh)
uniform_mesh.uniform_meshing(refine=3)
elif domain == 'partition2':
vertices = np.array([(0.0, 0.0), (0.5, 0.0), (1.0, 0.0),
(1.0, 0.5), (1.0, 1.0), (0.5, 1.0),
(0.0, 1.0), (0.0, 0.5), (0.5, 0.5)],
dtype=np.float)
facets = np.array([(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6),
(6, 7), (7, 0), (1, 8), (8, 7), (8, 3), (8, 5)],
dtype=np.int)
subdomain = np.array([(1, 0), (2, 0), (2, 0), (3, 0), (3, 0),
(4, 0), (4, 0), (1, 0), (1, 2), (1, 4),
(3, 2), (4, 3)],
dtype=np.int)
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain)
uniform_mesh = CVTPMesher(mgesh)
uniform_mesh.uniform_meshing(refine=2)
elif domain == 'hole1':
vertices = np.array([(0.0, 0.0), (0.5, 0.0), (1.0, 0.0),
(1.0, 0.5), (1.0, 1.0), (0.5, 1.0),
(0.0, 1.0), (0.0, 0.5), (0.4, 0.4),
(0.7, 0.4), (0.7, 0.7), (0.4, 0.7)],
dtype=np.float)
facets = np.array([(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6),
(6, 7), (7, 0), (8, 9), (9, 10), (10, 11),
(11, 8)],
dtype=np.int)
subdomain = np.array([(1, 0), (1, 0), (1, 0), (1, 0), (1, 0),
(1, 0), (1, 0), (1, 0), (1, -1), (1, -1),
(1, -1), (1, -1)],
dtype=np.int)
"""
vertices = np.array([
( 0.0, 0.0),( 1.0, 0.0),( 1.0, 1.0),( 0.0, 1.0),
( 0.4, 0.4),( 0.7, 0.4),( 0.7, 0.7),( 0.4, 0.7)],dtype=np.float)
facets = np.array([
(0, 1),(1, 2),( 2, 3),( 3, 0),
(4, 5),(5, 6),( 6, 7),( 7, 4)], dtype=np.int)
subdomain = np.array([
(1, 0),(1, 0),(1, 0),(1, 0),
(1,-1),(1,-1),(1,-1),(1,-1)], dtype=np.int)
"""
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain)
uniform_mesh = CVTPMesher(mesh)
uniform_mesh.uniform_meshing(refine=1)
mesh.print()
vor, start = uniform_mesh.voronoi()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, color='k', showindex=True)
mesh.find_node(axes, node=vor.points, showindex=True)
voronoi_plot_2d(vor, ax=axes)
plt.show()
fig = plt.figure()
axes = fig.gca()
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
plt.show()
i = 0
while i < 100:
vor = uniform_mesh.Lloyd(vor, start)
i += 1
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, color='k', showindex=True)
mesh.find_node(axes, node=vor.points, showindex=True)
voronoi_plot_2d(vor, ax=axes)
plt.show()
def uniform_meshing_test(self,
domain='square',
plot=True,
interior_nodes=True,
add_cnode=False):
if domain == 'square':
vertices = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0),
(0.0, 1.0)],
dtype=np.float)
facets = np.array([(0, 1), (1, 2), (2, 3), (3, 0)], dtype=np.int)
subdomain = np.array([(1, 0), (1, 0), (1, 0), (1, 0)],
dtype=np.int)
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain)
uniform_mesh = CVTPMesher(mesh)
uniform_mesh.uniform_boundary_meshing(n=2)
bnode = uniform_mesh.bnode
elif domain == 'LShape':
vertices = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0),
(0.0, 1.0), (-1.0, 1.0), (-1.0, 0.0),
(-1.0, -1.0), (0.0, -1.0)],
dtype=np.float)
fixed = np.array([0, 0, 0, 1, 0, 1, 0, 0], dtype=np.bool)
facets = np.array([(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6),
(6, 7), (7, 0)],
dtype=np.int)
subdomain = np.array([(1, 0), (1, 0), (1, 0), (1, 0), (1, 0),
(1, 0), (1, 0), (1, 0)],
dtype=np.int)
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain,
fixed)
uniform_mesh = CVTPMesher(mesh)
uniform_mesh.uniform_boundary_meshing(n=2)
bnode = uniform_mesh.bnode
elif domain == 'circle':
n = 20
h = 2 * np.pi / n
theta = np.arange(0, 2 * np.pi, h)
vertices = np.zeros((n, 2), dtype=np.float)
vertices[:, 0] = np.cos(theta)
vertices[:, 1] = np.sin(theta)
fixed = np.zeros(n, dtype=np.bool)
facets = np.zeros((n, 2), dtype=np.int)
facets[:, 0] = range(0, n)
facets[:-1, 1] = range(1, n)
subdomain = np.zeros((n, 2), dtype=np.int)
subdomain[:, 0] = 1
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain,
fixed)
uniform_mesh = CVTPMesher(mesh)
uniform_mesh.uniform_boundary_meshing(n=0)
bnode = uniform_mesh.bnode
elif domain == 'partition1':
vertices = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0),
(0.0, 1.0), (0.5, 0.5)],
dtype=np.float)
facets = np.array([(0, 1), (1, 2), (2, 3), (3, 0), (0, 4), (4, 3),
(4, 1), (4, 2)],
dtype=np.int)
subdomain = np.array([(1, 0), (2, 0), (3, 0), (4, 0), (4, 1),
(4, 3), (2, 1), (3, 2)],
dtype=np.int)
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain)
uniform_mesh = CVTPMesher(mesh)
uniform_mesh.uniform_boundary_meshing(n=3)
bnode = uniform_mesh.bnode
elif domain == 'partition2':
vertices = np.array([(0.0, 0.0), (0.5, 0.0), (1.0, 0.0),
(1.0, 0.5), (1.0, 1.0), (0.5, 1.0),
(0.0, 1.0), (0.0, 0.5), (0.5, 0.5)],
dtype=np.float)
facets = np.array([(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6),
(6, 7), (7, 0), (1, 8), (8, 7), (8, 3), (8, 5)],
dtype=np.int)
subdomain = np.array([(1, 0), (2, 0), (2, 0), (3, 0), (3, 0),
(4, 0), (4, 0), (1, 0), (1, 2), (1, 4),
(3, 2), (4, 3)],
dtype=np.int)
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain)
uniform_mesh = CVTPMesher(mesh)
uniform_mesh.uniform_boundary_meshing(n=2)
bnode = uniform_mesh.bnode
elif domain == 'hole1':
vertices = np.array([(0.0, 0.0), (0.5, 0.0), (1.0, 0.0),
(1.0, 0.5), (1.0, 1.0), (0.5, 1.0),
(0.0, 1.0), (0.0, 0.5), (0.4, 0.4),
(0.7, 0.4), (0.7, 0.7), (0.4, 0.7)],
dtype=np.float)
facets = np.array([(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6),
(6, 7), (7, 0), (8, 9), (9, 10), (10, 11),
(11, 8)],
dtype=np.int)
subdomain = np.array([(1, 0), (1, 0), (1, 0), (1, 0), (1, 0),
(1, 0), (1, 0), (1, 0), (1, -1), (1, -1),
(1, -1), (1, -1)],
dtype=np.int)
"""
vertices = np.array([
( 0.0, 0.0),( 1.0, 0.0),( 1.0, 1.0),( 0.0, 1.0),
( 0.4, 0.4),( 0.7, 0.4),( 0.7, 0.7),( 0.4, 0.7)],dtype=np.float)
facets = np.array([
(0, 1),(1, 2),( 2, 3),( 3, 0),
(4, 5),(5, 6),( 6, 7),( 7, 4)], dtype=np.int)
subdomain = np.array([
(1, 0),(1, 0),(1, 0),(1, 0),
(1,-1),(1,-1),(1,-1),(1,-1)], dtype=np.int)
"""
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain)
uniform_mesh = CVTPMesher(mesh)
uniform_mesh.uniform_boundary_meshing(n=1)
bnode = uniform_mesh.bnode
elif domain == 'hole2':
"""
vertices = np.array([
( 0.0, 0.0),( 0.5, 1.0),( 1.0, 0.0),( 1.5, 0.0),
( 2.0, 0.0),( 2.0, 0.5),( 2.0, 1.0),( 2.0, 1.5),
( 2.0, 2.0),( 1.5, 2.0),( 1.0, 2.0),( 0.5, 2.0),
( 0.0, 2.0),( 0.0, 1.5),( 0.0, 1.0),( 0.0, 0.5),
( 0.4, 0.4),( 0.4, 0.7),( 0.7, 0.7),( 0.7, 0.4),
( 1.2, 1.2),( 1.2, 1.5),( 1.5, 1.5),( 1.5, 1.2)],dtype=np.float)
facets = np.array([
( 0, 1),( 1, 2),( 2, 3),( 3, 4),
( 4, 5),( 5, 6),( 6, 7),( 7, 8),
( 8, 9),( 9,10),(10,11),(11,12),
(12,13),(13,14),(14,15),(15, 0),
(16,17),(17,18),(18,19),(19,16),
(20,21),(21,22),(22,23),(23,20)], dtype=np.int)
subdomain = np.array([
(1, 0),(1, 0),(1, 0),(1, 0),
(1, 0),(1, 0),(1, 0),(1, 0),
(1, 0),(1, 0),(1, 0),(1, 0),
(1, 0),(1, 0),(1, 0),(1, 0),
(1,-1),(1,-1),(1,-1),(1,-1),
(1,-2),(1,-2),(1,-2),(1,-2)], dtype=np.int)
"""
#"""
vertices = np.array(
[(0.0, 0.0), (1.0, 0.0), (2.0, 0.0), (2.0, 1.0), (2.0, 2.0),
(1.0, 2.0), (0.0, 2.0), (0.0, 1.0), (0.4, 0.4), (0.4, 0.7),
(0.7, 0.7), (0.7, 0.4), (1.2, 1.2), (1.2, 1.5), (1.5, 1.5),
(1.5, 1.2)],
dtype=np.float)
facets = np.array([
(0, 1),
(1, 2),
(2, 3),
(3, 4),
(4, 5),
(5, 6),
(6, 7),
(7, 0),
(8, 9),
(9, 10),
(10, 11),
(11, 8),
(12, 13),
(13, 14),
(14, 15),
(15, 12),
],
dtype=np.int)
subdomain = np.array([(1, 0), (1, 0), (1, 0), (1, 0), (1, 0),
(1, 0), (1, 0), (1, 0), (1, -1), (1, -1),
(1, -1), (1, -1), (1, -2), (1, -2), (1, -2),
(1, -2)],
dtype=np.int)
#"""
mesh = HalfEdgeMesh2d.from_edges(vertices, facets, subdomain)
uniform_mesh = CVTPMesher(mesh)
uniform_mesh.uniform_boundary_meshing(n=1)
bnode = uniform_mesh.bnode
if add_cnode == True:
cnode = uniform_mesh.cnode
bnode = np.append(bnode, cnode, axis=0)
vor = Voronoi(bnode, incremental=True)
if interior_nodes:
uniform_mesh.uniform_init_interior_nodes()
newnode = uniform_mesh.inode
for k in newnode:
vor.add_points(newnode[k])
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, color='k', showindex=True)
mesh.find_node(axes, node=bnode, showindex=True)
mesh.print()
voronoi_plot_2d(vor, ax=axes)
plt.show()
def run(self, estimator='mix'):
problem = self.problem
options = self.optoptions
moptions = self.moptions
model = problem['objective']
optalg = SteepestDescentAlg(problem, options)
x, f, g, diff = optalg.run(maxit=10)
q = np.zeros(model.rho.shape)
q[:, 0] = model.q0[:, -1]
q[:, 1] = model.q1[:, -1]
problem['x0'] = x
while True:
print('chiN', moptions['chiN'])
while True:
mesh = problem['mesh'] ##多边形网格
hmesh = HalfEdgeMesh2d.from_mesh(mesh) ##半边网格
aopts = hmesh.adaptive_options(method='mean',
maxcoarsen=3,
HB=True)
print('NN', mesh.number_of_nodes())
mu = problem['x0']
if estimator == 'mix':
eta = model.mix_estimate(q, w=1)
if estimator == 'grad':
eta = model.estimate(q)
aopts['data'] = {'mu': mu}
S0 = model.vemspace.project_to_smspace(aopts['data']['mu'][:,
0])
S1 = model.vemspace.project_to_smspace(aopts['data']['mu'][:,
1])
hmesh.adaptive(eta, aopts) ###半边网格做自适应
mesh = PolygonMesh.from_halfedgemesh(hmesh) ###多边形网格
model.reinit(mesh) ###多边形网格给进空间
aopts['data']['mu'] = np.zeros((model.gdof, 2))
aopts['data']['mu'][:, 0] = model.vemspace.interpolation(
S0, aopts['HB'])
aopts['data']['mu'][:, 1] = model.vemspace.interpolation(
S1, aopts['HB'])
problem['x0'] = aopts['data']['mu']
optalg = SteepestDescentAlg(problem, options)
x, f, g, diff = optalg.run(maxit=200)
problem['mesh'] = mesh ###多边形网格
problem['x0'] = x
problem['rho'] = model.rho
self.problem = problem
q = np.zeros(model.rho.shape)
q[:, 0] = model.q0[:, -1]
q[:, 1] = model.q1[:, -1]
if diff < options['FunValDiff']:
if (np.max(problem['rho'][:, 0]) < 1) and (np.min(
problem['rho'][:, 0]) > 0):
break
myfile = open(
moptions['rdir'] + '/' + str(int(moptions['chiN'])) +
'mesh.bin', 'wb')
import pickle
pickle.dump(problem['mesh'], myfile)
myfile.close()
model.save_data(moptions['rdir'] + '/' +
str(int(moptions['chiN'])) + '.mat')
moptions['chiN'] += 5
if moptions['chiN'] > 60:
break
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 = [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)
print('c', aopts['HB'])
print(mesh.ds.hcell)
#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)
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 1:
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 1:
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)
clevel = mesh.celldata['level']
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)
mesh.print()
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)
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 run(self, estimator='grad'):
problem = self.problem
options = self.optoptions
moptions = self.moptions
model = problem['objective']
mesh = problem['mesh']
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes, cellcolor='w')
plt.show()
#plt.savefig('flower15.png')
#plt.savefig('flower15.pdf')
#plt.close()
optalg = SteepestDescentAlg(problem, options)
x, f, g, diff = optalg.run(maxit=500)
q = np.zeros(model.rho.shape)
while True:
print('chiN', moptions['chiN'])
if moptions['chiN'] > 15:
optalg = SteepestDescentAlg(problem, options)
x, f, g, diff = optalg.run(maxit=10, eta_ref='etamaxmin')
q = np.zeros(model.rho.shape)
q[:, 0] = model.q0[:, -1]
q[:, 1] = model.q1[:, -1]
problem['x0'] = x
while True:
mesh = problem['mesh']
hmesh = HalfEdgeMesh2d.from_mesh(mesh)
aopts = hmesh.adaptive_options(method='mean',
maxcoarsen=3,
HB=True)
print('NN', mesh.number_of_nodes())
mu = problem['x0']
if estimator == 'mix':
eta = model.mix_estimate(q, w=1)
if estimator == 'grad':
eta = model.estimate(q)
aopts['data'] = {'mu': mu}
S0 = model.vemspace.project_to_smspace(aopts['data']['mu'][:,
0])
S1 = model.vemspace.project_to_smspace(aopts['data']['mu'][:,
1])
hmesh.adaptive(eta, aopts)
mesh = PolygonMesh.from_halfedgemesh(hmesh)
model.reinit(mesh)
aopts['data']['mu'] = np.zeros((model.gdof, 2))
aopts['data']['mu'][:, 0] = model.vemspace.interpolation(
S0, aopts['HB'])
aopts['data']['mu'][:, 1] = model.vemspace.interpolation(
S1, aopts['HB'])
problem['x0'] = aopts['data']['mu']
optalg = SteepestDescentAlg(problem, options)
x, f, g, diff = optalg.run(maxit=100)
problem['mesh'] = mesh
problem['x0'] = x
problem['rho'] = model.rho
q = np.zeros(model.rho.shape)
q[:, 0] = model.q0[:, -1]
q[:, 1] = model.q1[:, -1]
if diff < options['FunValDiff']:
if (np.max(problem['rho'][:, 0]) < 1) and (np.min(
problem['rho'][:, 0]) > 0):
break
myfile = open(
moptions['rdir'] + '/' + str(int(moptions['chiN'])) +
'mesh.bin', 'wb')
import pickle
pickle.dump(problem['mesh'], myfile)
myfile.close()
model.save_data(moptions['rdir'] + '/' +
str(int(moptions['chiN'])) + '.mat')
moptions['chiN'] += 1
if moptions['chiN'] > 60:
break
from HHOStokesSpace2d import HHOStokesSpace2d from Stokes2DData import Stokes2DData_0 # --- begin --- # n = 2 p = 1 nu = 1.0 pde = Stokes2DData_0(nu) # create pde model # --- mesh setting --- # box = [0, 1, 0, 1] # [0, 1]^2 domain mf = MeshFactory() meshtype = 'quad' mesh = mf.boxmesh2d(box, nx=n, ny=n, meshtype=meshtype) mesh = HalfEdgeMesh2d.from_mesh(mesh) mesh.init_level_info() mesh.uniform_refine(n-2) # refine the mesh at beginning # --- plot the mesh --- # # fig = plt.figure() # axes = fig.gca() # mesh.add_plot(axes, cellcolor='w') # find_entity(axes, mesh, entity='cell', showindex=True, color='b', markersize=10, fontsize=8) # find_entity(axes, mesh, entity='edge', showindex=True, color='r', markersize=10, fontsize=8) # find_entity(axes, mesh, entity='node', showindex=True, color='y', markersize=10, fontsize=8) # plt.show() cell2edge, cellLocation = mesh.ds.cell_to_edge() # # # #
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)
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)
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()