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=0, 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)
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
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(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 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 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 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, 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([(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 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 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]])
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)
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=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 = 4
ny = 4
mesh = StructureQuadMesh(self.box, nx, ny)
mesh.uniform_refine(n)
return mesh
elif meshtype == 'poly':
cell = np.array([
(1, 2, 0),
(3, 0, 2)], 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 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 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 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())
edge2cell = mesh.ds.edge_to_cell() # (NE, 4) edge2node = mesh.ds.edge_to_node() # edge edge2edge = mesh.ds.edge_to_edge() # sparse, (NE, NE) node2cell = mesh.ds.node_to_cell() # sparse, (NN, NC) node2edge = mesh.ds.node_to_edge() # sparse, (NN, NE) node2node = mesh.ds.node_to_node() # sparse, (NN, NN) isBdNode = mesh.ds.boundary_node_flag() # (NN, ), bool isBdEdge = mesh.ds.boundary_edge_flag() # (NE, ), bool isBdCell = mesh.ds.boundary_cell_flag() # (NC, ), bool bdNodeIdx = mesh.ds.boundary_node_index() # bdEdgeIdx = mesh.ds.boundary_edge_index() # bdCellIdx = mesh.ds.boundary_cell_index() # mesh.uniform_refine(1) 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()
from fealpy.mesh import TriangleMesh, TriangleMeshWithInfinityNode
from fealpy.decorator import cartesian, barycentric
# --- mesh
n = 0
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)
# --- to pmesh
# nmesh = TriangleMeshWithInfinityNode(mesh)
# pnode, pcell, pcellLocation = nmesh.to_polygonmesh()
# pmesh = PolygonMesh(pnode, pcell, pcellLocation)
# mesh = pmesh
# ---- plot mesh ----
# fig1 = plt.figure()
# axes = fig1.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()
node[0, :] = [0, 0, r]
node[1:, 0] = 15*np.cos(theta)
node[1:, 1] = 15*np.sin(theta)
node[1:, 2] = h
cell = np.array([
(0, 1, 2), (0, 2, 3), (0, 3, 4),
(0, 4, 5), (0, 5, 6), (0, 6, 1)
], dtype=np.int32)
surface = Sphere(c, r)
circle = Circle(radius=rc)
mesh = TriangleMesh(node, cell)
for i in range(8):
mesh.uniform_refine()
isBdNode = mesh.ds.boundary_node_flag()
r0 = np.sqrt(np.sum(mesh.node[isBdNode, 0:2]**2, axis=1))
mesh.node[isBdNode, 0:2] *=rc/r0.reshape(-1, 1)
mesh.node, _ = surface.project(mesh.node)
mesh0 = TriangleMesh(mesh.node.copy(), mesh.ds.cell.copy())
mesh0.node *=(r+0.03)/r
mesh1 = TriangleMesh(mesh.node.copy(), mesh.ds.cell.copy())
mesh1.node *=(r-0.03)/r
fig = plt.figure()
axes = fig.add_subplot(111, projection='3d')
#mesh.add_plot(axes)
return val
def f2(p):
x = p[..., 0]
y = p[..., 1]
val = np.exp(5 * (x**2 + (y - 1)**2)) / np.exp(10)
return val
theta = 0.35
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(4)
integrator = mesh.integrator(3)
node = mesh.entity('node')
cell = mesh.entity('cell')
tmesh = Tritree(node, cell)
femspace = LagrangeFiniteElementSpace(mesh, p=1)
integralalg = FEMeshIntegralAlg(integrator, mesh)
qf = integrator
bcs, ws = qf.quadpts, qf.weights
u1 = femspace.interpolation(f1)
grad = femspace.grad_value(u1, bcs, cellidx=None)
import numpy as np
import matplotlib.pyplot as plt
from fealpy.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)
tmesh = TriangleMesh(node, cell)
tmesh.uniform_refine(2)
node = tmesh.entity('node')
cell = tmesh.entity('cell')
fig = plt.figure()
axes = fig.gca()
tmesh.add_plot(axes)
tmesh.find_node(axes, showindex=True)
tmesh.find_edge(axes, showindex=True)
tmesh.find_cell(axes, showindex=True)
plt.show()
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()
fig = plt.figure()
import numpy as np
import matplotlib.pyplot as plt
from fealpy.mesh import TriangleMesh
# 网格节点数组
node = np.array([[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]],
dtype=np.float)
# 网格单元数组
cell = np.array([[1, 2, 0], [3, 0, 2]], dtype=np.int32)
mesh = TriangleMesh(node, cell)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
nodeIMatrix, cellIMatrix = mesh.uniform_refine(returnim=True)
print(nodeIMatrix[0].toarray())
print(cellIMatrix[0].toarray())
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
