def triangle_mesh_test(self, plot=False):
node = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0)])
cell = np.array([(1, 2, 0), (3, 0, 2)])
tmesh = TriangleMesh(node, cell)
tmesh.uniform_refine(n=1)
mesh = HalfEdgeMesh.from_mesh(tmesh)
if plot:
halfedge = mesh.ds.halfedge
for i, idx in enumerate(halfedge):
print(i, ": ", idx)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
fig = plt.figure()
axes = fig.gca()
mesh.add_halfedge_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def refine_triangle_rbTest(self, l, 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)
mesh = TriangleMesh(node, cell)
#mesh.uniform_refine()
mesh = HalfEdgeMesh.from_mesh(mesh)
mesh.ds.cell2hedge = np.array([0, 3, 2, 11, 10])
c = np.array([0.2, 0.2])
r = 1.2
h = 1e-2
k = 0
NB = 0
start = time.time()
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
if rb:
mesh.refine_triangle_rb(markedcell1)
else:
mesh.refine_triangle_rbg(markedcell1)
k += 1
print('循环', k, '次***************************')
#print('node', node)
#print('cell',cell)
end = time.time()
print(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)
plt.show()
if 0:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
cindex = np.arange(mesh.number_of_cells() - 1) + 1
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 = mesh.nodedata['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()
def voronoi_test(self, plot=False):
from scipy.spatial import Delaunay
from scipy.spatial import Voronoi, voronoi_plot_2d
from scipy.spatial import KDTree
points = np.random.rand(10, 2)
print(points)
# 边界点固定标记, 在网格生成与自适应算法中不能移除
# 1: 固定
# 0: 自由
fflag = np.ones(4, dtype=np.bool)
# dflag 单元所处的子区域的标记编号
# 0: 表示外部无界区域
# -n: n >= 1, 表示编号为 -n 洞
# n: n >= 1, 表示编号为 n 的内部子区域
dflag = np.array([1, 0])
node = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0)],
dtype=np.float)
halfedge = np.array([(1, 0, 1, 3, 4, 1), (2, 0, 2, 0, 5, 1),
(3, 0, 3, 1, 6, 1), (0, 0, 0, 2, 7, 1),
(0, 1, 7, 5, 0, 0), (1, 1, 4, 6, 1, 0),
(2, 1, 5, 7, 2, 0), (3, 1, 6, 4, 3, 0)],
dtype=np.int)
NC = 1
mesh = HalfEdgeMesh(node, halfedge, NC)
mesh.set_data('fflag', fflag, 'node')
mesh.set_data('dflag', dflag, 'cell')
v = Voronoi(points)
tree = KDTree(points)
print("points:\n", v.points)
print('vertices:\n', v.vertices)
print('ridge_points:\n', v.ridge_points)
print('ridge_vertices:\n', v.ridge_vertices)
print('regions:\n', v.regions)
print('point_region:\n', v.point_region)
d, nidx = tree.query(node)
print(nidx)
if plot:
halfedge = mesh.ds.halfedge
for i, idx in enumerate(halfedge):
print(i, ": ", idx)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
# mesh.find_node(axes, showindex=True, multiindex=nidx)
mesh.find_node(axes, node=points, color='r', showindex=True)
mesh.find_node(axes, node=v.vertices, color='b', showindex=True)
voronoi_plot_2d(v, axes)
fig = plt.figure()
axes = fig.gca()
mesh.add_halfedge_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def refine_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.uniform_refine()
mesh = HalfEdgeMesh.from_mesh(mesh)
c = np.array([0.8, 0.8])
r = 0.5
h = 1e-2
l = 6
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)
k += 1
print('循环', k, '次***************************')
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)
plt.show()
if 0:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
cindex, = np.nonzero(mesh.ds.cflag)
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 = mesh.nodedata['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()
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 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
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 run(self, estimator='mix'):
model = problem['objective']
mesh = problem['mesh']
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)
aopts = mesh.adaptive_options(method='numrefine',
maxcoarsen=3,
HB=True)
while True:
while True:
print('NN', mesh.number_of_nodes())
NC = mesh.number_of_cells()
mu = problem['x0']
w = np.zeros(mu.shape)
w[:, 0] = mu[:, 0] - mu[:, 1]
w[:, 1] = mu[:, 0] + mu[:, 1]
if estimator == 'mix':
#eta = model.mix_estimate(q,w=1)
eta = np.ones(NC, dtype=int)
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])
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)
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()
problem['mesh'] = mesh
problem['x0'] = x
q = model.rho.copy()
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
pass
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 = HalfEdgeMesh.from_polygonmesh(mesh)
NE = mesh.number_of_edges()
NC = mesh.number_of_cells()
if True:
isMarkedCell = np.zeros(NC + 1, dtype=np.bool)
isMarkedCell[2] = True
mesh.refine(isMarkedCell, dflag=False)
if True:
NC = mesh.number_of_cells()
isMarkedCell = np.zeros(NC + 1, dtype=np.bool)
isMarkedCell[6] = True
mesh.refine(isMarkedCell, dflag=False)
if True:
NC = mesh.number_of_cells()
isMarkedCell = np.zeros(NC + 1, dtype=np.bool)
isMarkedCell[3] = True
mesh.refine(isMarkedCell, dflag=False)
if True:
NC = mesh.number_of_cells()
isMarkedCell = np.zeros(NC + 1, dtype=np.bool)
isMarkedCell[1] = True
isMarkedCell[5] = True
mesh.refine(isMarkedCell, dflag=False)
if True:
NC = mesh.number_of_cells()
isMarkedCell = np.zeros(NC + 1, dtype=np.bool)
isMarkedCell[1] = True
isMarkedCell[12] = True
mesh.refine(isMarkedCell, dflag=False)
if True:
NC = mesh.number_of_cells()
isMarkedCell = np.zeros(NC + 1, dtype=np.bool)
isMarkedCell[0] = True
isMarkedCell[21] = True
mesh.refine(isMarkedCell, dflag=False)
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_edge(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()