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 init_mesh(self, n=4, meshtype='tri'):
node = np.array([(-1, -1), (0, -1), (-1, 0), (0, 0), (1, 0), (-1, 1),
(0, 1), (1, 1)],
dtype=np.float64)
if meshtype == 'tri':
cell = np.array([(1, 3, 0), (2, 0, 3), (3, 6, 2), (5, 2, 6),
(4, 7, 3), (6, 3, 7)],
dtype=np.int_)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n)
return mesh
elif meshtype == 'quadtree':
cell = np.array([(0, 1, 3, 2), (2, 3, 6, 5), (3, 4, 7, 6)],
dtype=np.int_)
mesh = Quadtree(node, cell)
mesh.uniform_refine(n)
return mesh
elif meshtype == 'tritree':
cell = np.array([(1, 3, 0), (2, 0, 3), (3, 6, 2), (5, 2, 6),
(4, 7, 3), (6, 3, 7)],
dtype=np.int_)
mesh = Tritree(node, cell)
mesh.uniform_refine(n)
return mesh
else:
raise ValueError("I don't know the meshtype %s".format(meshtype))
def init_mesh(self, n=4):
from ..mesh import TriangleMesh
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float)
cell = np.array([(1, 2, 0), (3, 0, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n)
return mesh
def to_conformmesh(self):
NN = self.number_of_nodes()
NE = self.number_of_edges()
NC = self.number_of_cells()
node = self.entity('node')
edge = self.entity('edge')
cell = self.entity('cell')
isLeafCell = self.is_leaf_cell()
edge2cell = self.ds.edge_to_cell()
flag0 = isLeafCell[edge2cell[:, 0]] & (~isLeafCell[edge2cell[:, 1]])
flag1 = isLeafCell[edge2cell[:, 1]] & (~isLeafCell[edge2cell[:, 0]])
LCell = edge2cell[flag0, 0]
RCell = edge2cell[flag1, 1]
isLeafCell = self.is_leaf_cell()
idx0 = edge2cell[flag0, 0]
N0 = len(idx0)
cell20 = np.zeros((2 * N0, 3), dtype=self.itype)
cell20[0:N0, 0] = edge[flag0, 0]
cell20[0:N0, 1] = cell[self.child[edge2cell[flag0, 1], 3],
edge2cell[flag0, 3]]
cell20[0:N0, 2] = cell[idx0, edge2cell[flag0, 2]]
cell20[N0:2 * N0, 0] = edge[flag0, 1]
cell20[N0:2 * N0, 1] = cell[self.child[edge2cell[flag0, 1], 3],
edge2cell[flag0, 3]]
cell20[N0:2 * N0, 2] = cell[idx0, edge2cell[flag0, 2]]
idx1 = edge2cell[flag1, 1]
N1 = len(idx1)
cell21 = np.zeros((2 * N1, 3), dtype=self.itype)
cell21[0:N1, 0] = edge[flag1, 1]
cell21[0:N1, 1] = cell[self.child[edge2cell[flag1, 0], 3],
edge2cell[flag1, 2]]
cell21[0:N1, 2] = cell[idx1, edge2cell[flag1, 3]]
cell21[N1:2 * N1, 0] = edge[flag1, 0]
cell21[N1:2 * N1, 1] = cell[self.child[edge2cell[flag1, 0], 3],
edge2cell[flag1, 2]]
cell21[N1:2 * N1, 2] = cell[idx1, edge2cell[flag1, 3]]
isLRCell = np.zeros(NC, dtype=np.bool)
isLRCell[LCell] = True
isLRCell[RCell] = True
idx = np.arange(NC)
cell0 = cell[(~isLRCell) & (isLeafCell)]
idx0 = idx[(~isLRCell) & (isLeafCell)]
cell = np.r_['0', cell0, cell20, cell21]
tmesh = TriangleMesh(node, cell)
tmesh.celldata['idxmap'] = np.r_['0', idx0, LCell, RCell, LCell,
RCell] #现在的cell单元与原来树结构中cell的对应关系.
return tmesh
def init_mesh(self, n=4, meshtype='tri'):
""" generate the initial mesh
"""
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float)
cell = np.array([(1, 2, 0), (3, 0, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n)
return mesh
def init_mesh(self, n=2, meshtype='tri'):
node = np.array([(0.0, 0.0), (0.5, 0.0), (1.0, 0.0), (0.0, 0.5),
(0.5, 0.5), (1.0, 0.5), (0.0, 1.0), (0.5, 1.0),
(0.5, 1.0), (1.0, 1.0)],
dtype=np.float)
cell = np.array([(3, 0, 4), (1, 4, 0), (4, 1, 5), (2, 5, 1), (6, 3, 7),
(4, 7, 3), (8, 4, 9), (5, 9, 4)],
dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n)
return mesh
def init_mesh(self, n=1, meshtype='tri'):
""" generate the initial mesh
"""
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float64)
if meshtype == 'tri':
cell = np.array([(1, 2, 0), (3, 0, 2)], dtype=np.int_)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n)
return mesh
else:
raise ValueError("".format)
def init_mesh(self, n=2, meshtype='tri', h=None):
""" generate the initial mesh
"""
from fealpy.mesh import TriangleMesh
node = np.array([(0, 0), (-1, -1), (0, -2), (1, -1), (2, 0), (1, 1),
(0, 2), (-1, 1)],
dtype=np.float)
cell = np.array([(1, 2, 0), (3, 0, 2), (4, 5, 3), (0, 3, 5), (5, 6, 0),
(7, 0, 6)],
dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n=n)
return mesh
def init_mesh(self, n=1, meshtype='tri'):
node = np.array([
(-1, -1),
( 0, -1),
( 1, -1),
(-1, 0),
( 0, 0),
( 1, 0),
(-1, 1),
( 0, 1)], dtype=np.float)
if meshtype == 'tri':
cell = np.array([
(3, 0, 4),
(1, 4, 0),
(4, 1, 5),
(2, 5, 1),
(6, 3, 7),
(4, 7, 3)], dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n)
return mesh
elif meshtype == 'poly':
cell = np.array([
(3, 0, 4),
(1, 4, 0),
(4, 1, 5),
(2, 5, 1),
(6, 3, 7),
(4, 7, 3)], dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n)
nmesh = TriangleMeshWithInfinityNode(mesh)
pnode, pcell, pcellLocation = nmesh.to_polygonmesh()
pmesh = PolygonMesh(pnode, pcell, pcellLocation)
return pmesh
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 init_mesh(self, n=4, meshtype='tri', h=0.1):
""" generate the initial mesh
"""
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float)
if meshtype == 'quadtree':
cell = np.array([(0, 1, 2, 3)], dtype=np.int)
mesh = Quadtree(node, cell)
mesh.uniform_refine(n)
return mesh
if meshtype == 'quad':
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1), (0.5, 0),
(1, 0.4), (0.3, 1), (0, 0.6), (0.5, 0.45)],
dtype=np.float)
cell = np.array([(0, 4, 8, 7), (4, 1, 5, 8), (7, 8, 6, 3),
(8, 5, 2, 6)],
dtype=np.int)
mesh = QuadrangleMesh(node, cell)
mesh.uniform_refine(n)
return mesh
elif meshtype == 'tri':
cell = np.array([(1, 2, 0), (3, 0, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n)
return mesh
elif meshtype == 'squad':
mesh = StructureQuadMesh([0, 1, 0, 1], h)
return mesh
else:
raise ValueError("".format)
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 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 init_mesh(self, meshdata=None):
import scipy.io as sio
from fealpy.mesh import TriangleMesh
if meshdata is None:
data = sio.loadmat('../fealpy/meshdata/saddle.mat')
else:
data = sio.loadmat(meshdata)
node = data['node']
cell = np.array(data['elem'], dtype=np.int64)
return TriangleMesh(node, cell)
def init_mesh(self, meshtype='tri', h=0.1):
""" generate the initial mesh
"""
from meshpy.triangle import build
domain = self.domain()
mesh = build(domain, max_volume=h**2)
node = np.array(mesh.points, dtype=np.float)
cell = np.array(mesh.elements, dtype=np.int)
if meshtype is 'tri':
mesh = TriangleMesh(node, cell)
return mesh
def show_basis(self, p=0):
h = 0.5
box = [-h, 1 + h, -h, 1 + h]
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([[1, 2, 0]], dtype=np.int)
mesh = TriangleMesh(node, cell)
space = RaviartThomasFiniteElementSpace2d(mesh, p=p)
fig = plt.figure()
space.show_basis(fig, box=box)
cell = np.array([[3, 0, 2]], dtype=np.int)
mesh = TriangleMesh(node, cell)
space = RaviartThomasFiniteElementSpace2d(mesh, p=p)
fig = plt.figure()
space.show_basis(fig, box=box)
print(space.bcoefs)
plt.show()
def init_mesh(self, n=2, meshtype='tri'):
""" generate the initial mesh
"""
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float)
cell = np.array([(1, 2, 0), (3, 0, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(2)
threshold = lambda p: (p[:, 0] > 0.25) & (p[:, 0] < 0.75) & (
p[:, 1] > 0.25) & (p[:, 1] < 0.75)
mesh.delete_cell(threshold)
mesh.uniform_refine(n=n)
return mesh
def Arctan(self, p=1, n=3):
pde = ArctanData()
node = np.array([[-1, -1], [1, -1], [1, 1], [-1, 1]], dtype=np.float_)
cell = np.array([[0, 1, 2], [0, 2, 3]], dtype=np.int_)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n=n)
space = LagrangeFiniteElementSpace(mesh, p=p)
uh = space.function()
A = space.stiff_matrix()
b = space.source_vector(pde.source)
bc = DirichletBC(space, pde.dirichlet)
A, b = bc.apply(A, b, uh)
uh[:] = spsolve(A, b).reshape(-1)
error0 = space.integralalg.L2_error(pde.solution, uh)
error1 = space.integralalg.L2_error(pde.gradient, uh.grad_value)
print(error0)
print(error1)
def opt_mesh(mesh):
p = mesh.p
surface = mesh.surface
NCN = mesh.number_of_corner_nodes()
node = mesh.entity('node')[:NCN].copy()
cell = mesh.entity('cell')[:, [0, -p - 1, -1]]
tmesh = TriangleMesh(node, cell)
alg = SurfaceTriangleMeshOptAlg(surface, tmesh)
alg.run(maxit=10)
node = alg.mesh.entity('node')
cell = alg.mesh.entity('cell')
mesh = LagrangeTriangleMesh(node, cell, p=p, surface=surface)
return mesh
def init_mesh(self):
from fealpy.mesh import TriangleMesh
t = (np.sqrt(5) - 1) / 2
point = np.array([[0, 1, t], [0, 1, -t], [1, t, 0], [1, -t, 0],
[0, -1, -t], [0, -1, t], [t, 0, 1], [-t, 0, 1],
[t, 0, -1], [-t, 0, -1], [-1, t, 0], [-1, -t, 0]],
dtype=np.float)
cell = np.array(
[[6, 2, 0], [3, 2, 6], [5, 3, 6], [5, 6, 7], [6, 0, 7], [3, 8, 2],
[2, 8, 1], [2, 1, 0], [0, 1, 10], [1, 9, 10], [8, 9, 1],
[4, 8, 3], [4, 3, 5], [4, 5, 11], [7, 10, 11], [0, 10, 7],
[4, 11, 9], [8, 4, 9], [5, 7, 11], [10, 9, 11]],
dtype=np.int)
point, d = self.project(point)
return TriangleMesh(point, cell)
def plot_basis(self, p=2, q=20, plot=True):
node = np.array([
(0.0, 0.0), (1.0, 0.0), (0.5, np.sqrt(3)/2)], dtype=np.float)
cell = np.array([(0, 1, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
space = LagrangeFiniteElementSpace(mesh, p=p)
bc = space.multi_index_matrix[1](q)/q
node = mesh.bc_to_point(bc) #( NQ, 1, 2)
phi = space.basis(bc) # (NQ, 1, ldof)
fig = plt.figure()
axes = fig.gca(projection='3d')
axes.plot_trisurf(
node[..., 0].reshape(-1),
node[..., 1].reshape(-1),
phi[..., 0].reshape(-1),
cmap='rainbow', lw=0.0, antialiased=True)
axes.plot_trisurf(
node[..., 0].reshape(-1),
node[..., 1].reshape(-1),
phi[..., 1].reshape(-1),
cmap='rainbow', lw=0.0, antialiased=True)
plt.show()
def lineTest(self):
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.uniform_refine(n=5)
point = np.array([[0.2, 0.5], [0.5, 0.8], [1.6, 0.5], [1.2, 0.2]])
segment = np.array([[0, 2], [1, 3]])
isCrossCell = mesh.find_crossed_cell(point, segment)
print(np.where(isCrossCell))
fig = plt.figure()
axes = fig.gca()
for i in range(len(segment)):
a = segment[i, 0]
b = segment[i, 1]
axes.plot(point[[a, b], 0], point[[a, b], 1], 'r')
mesh.add_plot(axes)
mesh.find_cell(axes, index=isCrossCell)
plt.show()
def init_mesh(self, n=1, meshtype='tri'):
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float)
if meshtype == 'tri':
cell = np.array([(1, 2, 0), (3, 0, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n)
return mesh
elif meshtype == 'quad':
nx = 2
ny = 2
mesh = StructureQuadMesh(self.box, nx, ny)
mesh.uniform_refine(n)
return mesh
def uniform_refine_test(self):
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)
N,C = mesh.uniform_refine(n=2,returnim = True)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_cell(axes)
plt.show()
print(N)
print(C.toarray())
def test_triangle_mesh():
from fealpy.mesh import TriangleMesh
node = np.array(
[
(0.0, 0.0), # 0 号点
(1.0, 0.0), # 1 号点
(1.0, 1.0), # 2 号点
(0.0, 1.0), # 3 号点
],
dtype=np.float64)
cell = np.array(
[
(1, 2, 0), # 0 号单元
(3, 0, 2), # 1 号单元
],
dtype=np.int_)
mesh = TriangleMesh(node, cell)
# 获取测试
assert id(node) == id(mesh.entity('node'))
assert id(cell) == id(mesh.entity('cell'))
edge = np.array([
[0, 1],
[2, 0],
[3, 0],
[1, 2],
[2, 3],
], dtype=np.int_)
assert np.all(edge == mesh.entity('edge'))
isBdNode = mesh.ds.boundary_node_flag()
assert np.all(isBdNode)
isBdEdge = mesh.ds.boundary_edge_flag()
assert isBdEdge.sum() == 4
assert isBdEdge[1] == False
cell2node = mesh.ds.cell_to_node()
cell2edge = mesh.ds.cell_to_edge()
cell2cell = mesh.ds.cell_to_cell()
edge2node = mesh.ds.edge_to_node()
edge2edge = mesh.ds.edge_to_edge()
edge2cell = mesh.ds.edge_to_cell()
node2node = mesh.ds.node_to_node()
node2edge = mesh.ds.node_to_edge()
node2cell = mesh.ds.node_to_cell()
# 加密测试
mesh.uniform_refine()
def init_mesh(self, n=2):
from ..mesh import TriangleMesh
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float)
cell = np.array([(1, 2, 0), (3, 0, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(n)
NN = mesh.number_of_nodes()
node = np.zeros((NN + 3, 2), dtype=np.float64)
node[:NN] = mesh.entity('node')
node[NN:] = node[[5], :]
cell = mesh.entity('cell')
cell[13][cell[13] == 5] = NN
cell[18][cell[18] == 5] = NN
cell[19][cell[19] == 5] = NN + 1
cell[12][cell[12] == 5] = NN + 1
cell[6][cell[6] == 5] = NN + 2
return TriangleMesh(node, cell)
def complex_mesh(r, filename):
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)
return pmesh
def triMesh(self, method='rg'):
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 = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
if method == 'rg':
halfedge = mesh.ds.halfedge
cstart = mesh.ds.cellstart
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
mesh.hedgecolor = color
elif method == 'nvb':
halfedge = mesh.ds.halfedge
cstart = mesh.ds.cellstart
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
color[[2, 3, 10, 11]] = 1
mesh.hedgecolor = color
return mesh
return False
def peak(p):
x = p[..., 0]
y = p[..., 1]
val = 3 * (1 - x)**2 * np.exp(-(x**2) - (y + 1)**2) - 10 * (
x / 5 - pow(x, 3) -
pow(y, 5)) * np.exp(-x**2 - y**2) - 1 / 3 * np.exp(-(x + 1)**2 - y**2)
return val
node = np.array([(-5, -5), (5, -5), (5, 5), (-5, 5)], dtype=np.float)
cell = np.array([(1, 2, 0), (3, 0, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(5)
node = mesh.entity('node')
cell = mesh.entity('cell')
tmesh = Tritree(node, cell)
femspace = LagrangeFiniteElementSpace(mesh, p=1)
uI = femspace.interpolation(peak)
estimator = Estimator(uI[:], mesh, 0.2, 0.5)
isExtremeNode = estimator.is_extreme_node()
print(isExtremeNode.sum())
tmesh.adaptive_refine(estimator)
mesh = estimator.mesh
isExtremeNode = estimator.is_extreme_node()
