def edge_to_cell_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 = HalfEdgePolygonMesh.from_polygonmesh(mesh)
NE = mesh.number_of_edges()
edge = mesh.entity('edge')
edge2cell = mesh.ds.edge_to_cell()
print('edge:')
for i in range(NE):
print(i, ":", edge[i], edge2cell[i])
NC = mesh.number_of_cells()
cell, cellLocation = mesh.entity('cell')
cell2edge = mesh.ds.cell_to_edge()
for i in range(NC):
print(i, ":", cell[cellLocation[i]:cellLocation[i + 1]])
print(i, ":", cell2edge[cellLocation[i]:cellLocation[i + 1]])
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()
def project_test(self, u, p=2, mtype=0, plot=True):
from fealpy.mesh.simple_mesh_generator import triangle
if mtype == 0:
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
dtype=np.float)
cell = np.array([0, 1, 2, 3], dtype=np.int)
cellLocation = np.array([0, 4], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
elif mtype == 1:
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
dtype=np.float)
cell = np.array([0, 1, 2, 3, 0, 2], dtype=np.int)
cellLocation = np.array([0, 3, 6], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
elif mtype == 2:
h = 0.025
mesh = triangle([-1, 1, -1, 1], h, meshtype='polygon')
elif mtype == 3:
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
dtype=np.float)
cell = np.array([[0, 1, 2, 3]], dtype=np.int)
mesh = QuadrangleMesh(node, cell)
mesh.uniform_refine()
mesh = PolygonMesh.from_mesh(mesh)
elif mtype == 4:
node = np.array([(-1, -1), (1, -1), (1, 0), (1, 1), (-1, 1),
(-1, 0)],
dtype=np.float)
cell = np.array([0, 1, 2, 5, 2, 3, 4, 5], dtype=np.int)
cellLocation = np.array([0, 4, 8], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
if True:
cell, cellLocation = mesh.entity('cell')
edge = mesh.entity('edge')
cell2edge = mesh.ds.cell_to_edge()
bc = mesh.entity_barycenter('edge')
uspace = ReducedDivFreeNonConformingVirtualElementSpace2d(mesh, p)
up = uspace.project(u)
up = uspace.project_to_smspace(up)
print(up)
integralalg = uspace.integralalg
error = integralalg.L2_error(u, up)
print(error)
A = uspace.matrix_A()
P = uspace.matrix_P()
sio.savemat('A.mat', {"A": A.toarray(), "P": P.toarray()})
if plot:
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()
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 project_test(self, u, p=2, mtype=0, plot=True):
from fealpy.mesh.simple_mesh_generator import triangle
if mtype == 0:
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
dtype=np.float)
cell = np.array([0, 1, 2, 3], dtype=np.int)
cellLocation = np.array([0, 4], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
elif mtype == 1:
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
dtype=np.float)
cell = np.array([0, 1, 2, 3, 0, 2], dtype=np.int)
cellLocation = np.array([0, 3, 6], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
elif mtype == 2:
h = 0.1
mesh = triangle([-1, 1, -1, 1], h, meshtype='polygon')
elif mtype == 3:
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
dtype=np.float)
cell = np.array([[0, 1, 2, 3]], dtype=np.int)
mesh = QuadrangleMesh(node, cell)
mesh.uniform_refine()
mesh = PolygonMesh.from_mesh(mesh)
cell, cellLocation = mesh.entity('cell')
edge = mesh.entity('edge')
cell2edge = mesh.ds.cell_to_edge()
uspace = DivFreeNonConformingVirtualElementSpace2d(mesh, p)
up = uspace.project(u)
print(up)
up = uspace.project_to_smspace(up)
print(up)
integralalg = uspace.integralalg
error = integralalg.L2_error(u, up)
print(error)
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()
def show_solution_test(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) / 2.0
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 = HalfEdgePolygonMesh.from_polygonmesh(mesh)
def u(p):
pi = np.pi
x = p[..., 0]
y = p[..., 1]
return np.sin(pi * x) * np.sin(pi * y)
node = mesh.entity('node')
solution = u(node)
plot = MatlabShow()
plot.show_solution(mesh, solution)
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()
