def my_test(n, interface, fname):
t0 = time.clock()
alg = InterfaceMesh2d(interface, interface.box, n)
ppoint, pcell, pcellLocation = alg.run()
t1 = time.clock()
pmesh = PolygonMesh(ppoint, pcell, pcellLocation)
a = pmesh.angle()
write_vtk_mesh(pmesh, fname)
return t1 - t0, np.max(a), (n+1)*(n+1)
def init_mesh(self, n=4, meshtype='tri', h=0.1):
""" generate the initial mesh
"""
from meshpy.triangle import build
domain = self.domain(domaintype='meshpy')
mesh = build(domain, max_volume=h**2)
node = np.array(mesh.points, dtype=np.float64)
cell = np.array(mesh.elements, dtype=np.int_)
if meshtype == 'tri':
return TriangleMesh(node, cell)
elif meshtype == 'polygon':
mesh = TriangleMeshWithInfinityNode(TriangleMesh(node, cell))
pnode, pcell, pcellLocation = mesh.to_polygonmesh()
return PolygonMesh(pnode, pcell, pcellLocation)
def loadMatlabMesh(self, filename=None):
# filename = self.filename if filename is None else filename
# mfile = self.mfile if filename is None else loadmat(filename)
mfile = loadmat(filename)
pnode = mfile['node']
pelem = mfile['elem']
Nelem = pelem.shape[0]
pcellLocation = np.zeros((Nelem + 1,), dtype=np.int)
pcell = np.zeros((0,), dtype=np.int)
for n in range(Nelem):
lcell = np.squeeze(pelem[n][0]) - 1 # let the index from 0.
lNedge = lcell.shape[0]
pcellLocation[n + 1] = pcellLocation[n] + lNedge
pcell = np.concatenate([pcell, lcell])
mesh = PolygonMesh(pnode, pcell, pcellLocation)
return mesh
import sys import numpy as np from fealpy.mesh.TriangleMesh import TriangleMeshWithInfinityPoint from fealpy.mesh import rectangledomainmesh from fealpy.mesh.PolygonMesh import PolygonMesh import matplotlib.pyplot as plt n = 2 box = [0, 1, 0, 1] mesh = rectangledomainmesh(box, nx=n, ny=n, meshtype='tri') nmesh = TriangleMeshWithInfinityPoint(mesh) ppoint, pcell, pcellLocation = nmesh.to_polygonmesh() pmesh = PolygonMesh(ppoint, pcell, pcellLocation)
for i in range(NNC):
idx0 = np.arange(newCellLocation2[i],
newCellLocation2[i] + location[i, 0] + 1)
idx1 = np.arange(initLocation[i], initLocation[i] + location[i, 0] + 1)
newCell2[idx0] = cell[idx1]
idx0 = np.arange(newCellLocation2[i] + location[i, 0] + 3,
newCellLocation2[i] + NV2[i])
idx1 = np.arange(initLocation[i] + location[i, 1] + 1,
initLocation[i] + NV0[i])
newCell2[idx0] = cell[idx1]
np.repeat(isInterfaceCell, NV)
NV3 = NV[~isInterfaceCell]
newCell3 = cell[np.repeat(~isInterfaceCell, NV)]
newCellLocation3 = np.zeros(NV3.shape[0] + 1, dtype=np.int)
newCellLocation3[1:] = np.cumsum(NV3)
cell = np.concatenate((newCell3, newCell1, newCell2))
cellLocation = np.concatenate(
(newCellLocation3[0:-1], newCellLocation3[-1] + newCellLocation1[0:-1],
newCellLocation3[-1] + newCellLocation1[-1] + newCellLocation2),
axis=0)
point = np.append(point, cutPoint, axis=0)
polymesh1 = PolygonMesh(point, cell, cellLocation)
fig = plt.figure()
axes = fig.gca()
polymesh1.add_plot(axes)
#polymesh.find_edge(axes, index=isCutEdge0, color='y')
plt.show()
from fealpy.mesh.PolygonMesh import PolygonMesh
node = np.array([(0, 0), (1, 0), (2, 0), (0, 1), (1, 1), (2, 1), (0, 2),
(1, 2), (2, 2)],
dtype=np.float)
cell = np.array([1, 4, 0, 3, 0, 4, 1, 2, 5, 4, 3, 4, 7, 6, 4, 5, 8, 7],
dtype=np.int)
cellLocation = np.array([0, 3, 6, 10, 14, 18], dtype=np.int)
node = np.array([(0, 0), (1, 0), (2, 0), (0, 1), (1, 1), (2, 1), (0, 2),
(1, 2), (2, 2)],
dtype=np.float)
cell = np.array([0, 3, 4, 1, 1, 4, 5, 2, 3, 6, 7, 4, 4, 7, 8, 5], dtype=np.int)
cellLocation = np.array([0, 4, 8, 12, 16], dtype=np.int)
pmesh = PolygonMesh(node, cell, cellLocation)
area = pmesh.cell_area()
d = pmesh.angle()
print(d)
print(pmesh.node)
print(pmesh.ds.cell)
print(pmesh.ds.edge)
print(pmesh.ds.edge2cell)
print(area)
print(pmesh.ds.cell_to_cell().toarray())
print(pmesh.ds.cell_to_node().toarray())
print(pmesh.ds.cell_to_edge().toarray())
fig = plt.figure()
axes = fig.gca()
from fealpy.mesh.curve import CircleCurve
from fealpy.mesh.curve import Curve1
from fealpy.mesh.curve import Curve2
from fealpy.mesh.curve import Curve3
import time
n = 40
interface = Curve1(a=6)
#interface = Curve2()
#interface = Curve3()
t0 = time.clock()
alg = InterfaceMesh2d(interface, interface.box, n)
ppoint, pcell, pcellLocation = alg.run()
t1 = time.clock()
pointMarker = alg.point_marker()
pmesh = PolygonMesh(ppoint, pcell, pcellLocation)
a = pmesh.angle()
print(a.max())
write_vtk_mesh(pmesh, 'test.vtk')
fig = plt.figure()
axes = fig.gca()
pmesh.add_plot(axes, cellcolor=[0.5, 0.9, 0.45])
pmesh.find_point(axes, point=pmesh.point[pointMarker], markersize=30)
plt.subplots_adjust(left=0, bottom=0, right=1, top=1, wspace=0, hspace=0)
plt.savefig('sixfolds.pdf')
plt.show()
pfix = np.array([[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]],
dtype=np.float)
fd = lambda p: drectangle(p, box)
pmesh = distmesh2d(fd, h, box, pfix, meshtype='polygon')
area = pmesh.entity_measure('cell')
node = pmesh.entity('node')
t = Delaunay(node)
tmesh = TriangleMesh(node, t.simplices.copy())
area = tmesh.entity_measure('cell')
tmesh.delete_cell(area < 1e-8)
area = tmesh.entity_measure('cell')
print(len(tmesh.node))
pmesh = PolygonMesh.from_mesh(tmesh)
print(pmesh.ds.cell)
fig = plt.figure()
axes = fig.gca()
pmesh.add_plot(axes)
#mesh.find_node(axes, showindex=True)
plt.show()
Ndof = np.zeros((maxit, ), dtype=np.int)
errorType = [
'$|| u - \Pi^\\nabla u_h||_0$ with p=1',
'$||\\nabla u - \\nabla \Pi^\\nabla u_h||_0$ with p=1',
]
p = 1
p = 1 # degree of the vem space
box = [0, 1, 0, 1] # domain
n = 10 # initial
maxit = 5
error = np.zeros((maxit,), dtype=np.float)
Ndof = np.zeros((maxit,), dtype=np.int)
model = CosCosData()
model = PolynomialData()
model = ExpData()
for i in range(maxit):
# Mesh
mesh0 = rectangledomainmesh(box, nx=n, ny=n, meshtype='tri')
mesh1 = TriangleMeshWithInfinityPoint(mesh0)
point, cell, cellLocation = mesh1.to_polygonmesh()
mesh = PolygonMesh(point, cell, cellLocation)
# VEM Space
V = VirtualElementSpace2d(mesh, p)
uh = FiniteElementFunction(V)
Ndof[i] = V.number_of_global_dofs()
vem = PoissonVEMModel(model, V)
BC = DirichletBC(V, model.dirichlet)
solve(vem, uh, dirichlet=BC, solver='direct')
# error
uI = V.interpolation(model.solution)
def tri_to_polygon(mesh):
nmesh = TriangleMeshWithInfinityPoint(mesh)
ppoint, pcell, pcellLocation = nmesh.to_polygonmesh()
return PolygonMesh(ppoint, pcell, pcellLocation)
p = 2 #int(sys.argv[2]) # 有限元空间的次数
maxit =4 #int(sys.argv[4]) # 迭代加密的次数
pde = PDE() # 创建 pde 模型
beta = 200
alpha = -1
# 误差类型与误差存储数组
errorType = ['$|| u - u_h||_0$', '$||\\nabla u - \\nabla u_h||_0$']
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
# 自由度数组
NDof = np.zeros(maxit, dtype=np.int)
for i in range(maxit):
print("The {}-th computation:".format(i))
mesh = pde.init_mesh(n=i+3, meshtype='tri')
mesh = PolygonMesh.from_mesh(mesh)
# mesh.add_plot(plt, cellcolor='w')
# mesh = pde.init_mesh(n=2**(i+3), meshtype='poly')
# mesh.add_plot(plt, cellcolor='w')
space = ScaledMonomialSpace2d(mesh,p)
NDof[i] = space.number_of_global_dofs()
fem = IPDGModel(pde, mesh, p) # 创建 Poisson 有限元模型
fem.solve(beta,alpha) # 求解
uh = fem.uh
errorMatrix[0, i] = space.integralalg.L2_error(pde.solution, uh)
errorMatrix[1, i] = space.integralalg.L2_error(pde.gradient, uh.grad_value)
# 显示误差
show_error_table(NDof, errorType, errorMatrix)
# 可视化误差收敛阶
import sys import matplotlib.pyplot as plt from fealpy.mesh.simple_mesh_generator import unitcircledomainmesh from fealpy.mesh.TriangleMesh import TriangleMeshWithInfinityPoint from fealpy.mesh.PolygonMesh import PolygonMesh h = 0.1 mesh0 = unitcircledomainmesh(h) mesh1 = TriangleMeshWithInfinityPoint(mesh0) point, cell, cellLocation = mesh1.to_polygonmesh() pmesh = PolygonMesh(point, cell, cellLocation) f0 = plt.figure() axes0 = f0.gca() mesh0.add_plot(axes0) f1 = plt.figure() axes1 = f1.gca() pmesh.add_plot(axes1) plt.show()
import numpy as np import matplotlib.pyplot as plt from fealpy.mesh.simple_mesh_generator import rectangledomainmesh from fealpy.mesh.TriangleMesh import TriangleMeshWithInfinityPoint from fealpy.mesh.PolygonMesh import PolygonMesh # Generate mesh box = [-1, 1, -1, 1] mesh = rectangledomainmesh(box, nx=10, ny=10, meshtype='tri') mesht = TriangleMeshWithInfinityPoint(mesh) ppoint, pcell, pcellLocation = mesht.to_polygonmesh() pmesh = PolygonMesh(ppoint, pcell, pcellLocation) # Virtual element space fig = plt.figure() axes = fig.gca() pmesh.add_plot(axes) plt.show()
# @E-mail: [email protected] # @Site: # @Time: Nov 01, 2020 # --- from scipy.io import loadmat import numpy as np from fealpy.mesh.PolygonMesh import PolygonMesh from ShowCls import ShowCls m = loadmat('../Meshfiles/Dmesh_nonconvex_[0,1]x[0,1]_4.mat') pnode = m['node'] pelem = m['elem'] Nelem = pelem.shape[0] pcellLocation = np.zeros((Nelem + 1, ), dtype=np.int) pcell = np.zeros((0, ), dtype=np.int) for n in range(Nelem): lcell = np.squeeze(pelem[n][0]) - 1 # let the index from 0. lNedge = lcell.shape[0] pcellLocation[n + 1] = pcellLocation[n] + lNedge pcell = np.concatenate([pcell, lcell]) # print('pcell = ', pcell) mesh = PolygonMesh(pnode, pcell, pcellLocation) sc = ShowCls(1, mesh) sc.showMesh() # --- print("End of this file")