def show_mesh(self, p=2, plot=True):
mf = MeshFactory()
mesh = mf.boxmesh2d([0, 1, 0, 1], nx=2, ny=2, meshtype='tri')
node = mesh.entity('node')
cell = mesh.entity('cell')
ltmesh = LagrangeTriangleMesh(node, cell, p=p)
NN = ltmesh.number_of_nodes()
mesh.ds.edge = ltmesh.lds.edge
mesh.ds.edge2cell = ltmesh.lds.edge2cell
node = ltmesh.entity('node')
#ltmesh.print()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, node=node, showindex=True, fontsize=28)
mesh.find_edge(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def save_mesh(self, p=2, fname='test.vtu'):
mf = MeshFactory()
mesh = mf.boxmesh2d([0, 1, 0, 1], nx=2, ny=2, meshtype='tri')
node = mesh.entity('node')
cell = mesh.entity('cell')
mesh = LagrangeTriangleMesh(node, cell, p=p)
mesh.to_vtk(fname=fname)
def init_mesh(self, n=0, h=0.005, nh=100, p=1):
fname = 'initial/file1.vtu'
data = meshio.read(fname)
node = data.points
cell = data.cells[0][1]
mesh = LagrangeTriangleMesh(node * 500, cell, p=p)
mesh.uniform_refine(n)
mesh = LagrangeWedgeMesh(mesh, h, nh, p=p)
self.mesh = mesh
self.p = p
return mesh
def test_lagrange_triangle_mesh(p):
from fealpy.mesh import LagrangeTriangleMesh
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 = LagrangeTriangleMesh(node, cell, p=p)
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()
def interpolation(self, p=2, n=1, fname='surface.vtu'):
from fealpy.geometry import SphereSurface
from fealpy.pde.surface_poisson_model_3d import SphereSinSinSinData
pde = SphereSinSinSinData()
surface = pde.domain()
mesh = pde.init_mesh(n=n)
node = mesh.entity('node')
cell = mesh.entity('cell')
mesh = LagrangeTriangleMesh(node, cell, p=p, surface=surface)
space = ParametricLagrangeFiniteElementSpace(mesh, p=p)
uI = space.interpolation(pde.solution)
mesh.nodedata['uI'] = uI[:]
error0 = space.integralalg.error(pde.solution, uI.value)
error1 = space.integralalg.error(pde.gradient, uI.grad_value)
print(error0, error1)
mesh.to_vtk(fname=fname)
def surface_area(self, p=2):
from fealpy.geometry import SphereSurface
surface = SphereSurface()
mesh = surface.init_mesh()
e = 0
maxit = 5
for i in range(maxit):
node = mesh.entity('node')
cell = mesh.entity('cell')
lmesh = LagrangeTriangleMesh(node, cell, p=p, surface=surface)
NC = lmesh.number_of_cells()
a = lmesh.cell_area()
a = sum(a)
a_e = (4 * np.pi)
e_new = abs(a - a_e)
order = np.log2(e / e_new)
e = e_new
print("e:", e)
print("0:", order)
if i < maxit - 1:
mesh.uniform_refine(surface=surface)
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 surface_mesh(self, p=2, fname='surface.vtu'):
from fealpy.geometry import SphereSurface, EllipsoidSurface, SphereSurfaceTest
surface = SphereSurface()
#surface = SphereSurfaceTest()
#surface = EllipsoidSurface()
#surface = ScaledSurface(surface,scale=[9,3,1])
mesh = surface.init_mesh()
node = mesh.entity('node')
cell = mesh.entity('cell')
lmesh = LagrangeTriangleMesh(node, cell, p=p, surface=surface)
NC = lmesh.number_of_cells()
a = lmesh.cell_area()
lmesh.to_vtk(fname=fname)
def init_mesh(self, meshtype='tri', returnnc=False, p=None):
if meshtype == 'tri':
t = (np.sqrt(5) - 1)/2
node = 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.float64)
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)
node, d = self.project(node)
if returnnc:
return node, cell
else:
if p is None:
from fealpy.mesh import TriangleMesh
return TriangleMesh(node, cell)
else:
from fealpy.mesh import LagrangeTriangleMesh
return LagrangeTriangleMesh(node, cell, p=p, surface=self)
elif meshtype == 'quad':
node = np.array([
(-1, -1, -1),
(-1, -1, 1),
(-1, 1, -1),
(-1, 1, 1),
(1, -1, -1),
(1, -1, 1),
(1, 1, -1),
(1, 1, 1)], dtype=np.float64)
cell = np.array([
(0, 1, 4, 5),
(6, 7, 2, 3),
(2, 3, 0, 1),
(4, 5, 6, 7),
(1, 3, 5, 7),
(2, 0, 6, 4)], dtype=np.int_)
node, d = self.project(node)
if returnnc:
return node, cell
else:
if p is None:
from fealpy.mesh import QuadrangleMesh
return QuadrangleMesh(node, cell)
else:
from fealpy.mesh import LagrangeQuadrangleMesh
return LagrangeQuadrangleMesh(node, cell, p=p, surface=self)
pde = PDE()
surface = pde.domain()
mesh = pde.init_mesh(n=n)
errorType = ['$|| u - u_h||_{\Omega,0}$'
]
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
NDof = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
print("The {}-th computation:".format(i))
node = mesh.entity('node')
cell = mesh.entity('cell')
lmesh = LagrangeTriangleMesh(node, cell, p=p, surface=surface)
space = IsoLagrangeFiniteElementSpace(lmesh, p=p)
NDof[i] = space.number_of_global_dofs()
qf = lmesh.integrator(q=p+3, etype='cell')
bcs, ws = qf.get_quadrature_points_and_weights()
Jh = lmesh.jacobi_matrix(bcs)
nh = np.cross(Jh[..., 0], Jh[..., 1], axis=-1)
val = np.sqrt(np.sum(nh**2, axis=-1))
nh[...,0] /=val
nh[...,1] /=val
nh[...,2] /=val
bc = lmesh.bc_to_point(bcs)
n = pde.normal(bc)
surface = pde.domain()
mesh = pde.init_mesh(n=n)
errorType = [
'$|| u - u_h||_{\Omega,0}$', '$||\\nabla u - \\nabla u_h||_{\Omega, 0}$',
'$|| u - u_I||_{\Omega,0}$', '$||\\nabla u - \\nabla u_I||_{\Omega, 0}$'
]
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
NDof = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
print("The {}-th computation:".format(i))
node = mesh.entity('node')
cell = mesh.entity('cell')
lmesh = LagrangeTriangleMesh(node, cell, p=p, surface=surface)
space = IsoLagrangeFiniteElementSpace(lmesh, p=p)
NDof[i] = space.number_of_global_dofs()
print(NDof[i])
uh = space.function()
A = space.stiff_matrix()
F = space.source_vector(pde.source)
# 封闭曲面，设置其第 0 个插值节点的值为真解值
bc = DirichletBC(space, pde.solution)
A, F = bc.apply(A, F, uh, threshold=np.array([0]))
uh[:] = spsolve(A, F).reshape(-1)
uI = space.interpolation(pde.solution)
errorMatrix[0, i] = space.integralalg.error(pde.solution,
pde = PDE()
surface = pde.domain()
mesh = pde.init_mesh(n=n)
errorType = ['$|| u - u_h||_{\Omega,0}$'
]
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
NDof = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
print("The {}-th computation:".format(i))
node = mesh.entity('node')
cell = mesh.entity('cell')
lmesh = LagrangeTriangleMesh(node, cell, p=p, surface=surface)
space = IsoLagrangeFiniteElementSpace(lmesh, p=p)
NDof[i] = space.number_of_global_dofs()
qf = lmesh.integrator(q=p+3, etype='cell')
bcs, ws = qf.get_quadrature_points_and_weights()
print('bcs', bcs.shape)
gphi = lmesh.grad_shape_function(bcs, p=p) #(NQ,NC,ldof,TD)
print('gphi', gphi.shape)
Jh = lmesh.jacobi_matrix(bcs)
print('Jh', Jh.shape)
bc = lmesh.bc_to_point(bcs)
print('bc', bc.shape)
val = np.sum(bc, axis =-1)
print('val', val.shape)
val1 = (Jh.T/val.T).T
#import scipy.io as sio
from fealpy.mesh import LagrangeTriangleMesh, MeshFactory, LagrangeWedgeMesh
from fealpy.writer import MeshWriter
#p = int(sys.argv[1])
#n = int(sys.argv[2])
#h = sys.argv[3]
#nh = int(sys.argv[4])
fname = 'initial/file1.vtu'
data = meshio.read(fname)
node = data.points
cell = data.cells[0][1]
mesh = LagrangeTriangleMesh(node*500, cell, p=1)
mesh.uniform_refine(n=0)
mesh = LagrangeWedgeMesh(mesh, h=0.005, nh=1, p=1)
edge = mesh.entity('edge')
node = mesh.entity('node')
cell = mesh.entity('cell')
tface, qface = mesh.entity('face')
print(tface.shape)
mesh.celldata['a'] = np.arange(len(cell))
mesh.to_vtk(fname='write.vtu')