def coarsen_poly(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.init_level_info()
isMarkedCell = np.array([0, 0, 0, 1, 0], dtype=np.bool_)
mesh.refine_poly(isMarkedCell)
NC = mesh.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[[1, 2, 3, 4, 5, 6]] = True
mesh.coarsen_poly(isMarkedCell)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
mesh.add_halfedge_plot(axes, showindex=True)
plt.show()
def coarsen_tri(self, maxit=2, method='rg', plot=True, rb=True):
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)
if True:
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
isMarkedCell = np.array([0, 1, 0, 0, 1], dtype=np.bool_)
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
mesh.hedgecolor = color
mesh.refine_triangle_rg(isMarkedCell)
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
if 0:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
if method == 'rg':
if 1:
NC = mesh.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[[1, 2, 5, 6, 7, 9]] = True
print('*************lll*********')
mesh.coarsen_triangle_rg(isMarkedCell)
if 1:
NC = mesh.number_of_all_cells()
isMarkedCell = np.zeros(NC, dtype=np.bool_)
isMarkedCell[[0, 1, 2, 3, 4, 5, 6, 7]] = True
print('*************lll*********')
mesh.coarsen_triangle_rg(isMarkedCell)
NC = mesh.number_of_all_cells()
isMarkedCell = np.ones(NC, dtype=np.bool_)
print('*************lll*********')
mesh.refine_triangle_rg(isMarkedCell)
else:
color[[2, 3, 10, 11]] = 1
mesh.hedgecolor = color
isMarkedCell = np.array([0, 1, 1, 0, 0], dtype=np.bool_)
#isMarkedCell = np.array([0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ,0],
# dtype=np.bool_)
mesh.refine_triangle_nvb(isMarkedCell)
mesh.print()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
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 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 coarsen_poly(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)
isMarkedCell = np.array([0,0,0,1,0], dtype=np.bool_)
mesh.refine_poly(isMarkedCell)
isMarkedCell = np.array([0,0,0,0,1,1,1], dtype=np.bool_)
mesh.coarsen_poly(isMarkedCell)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
edge = totalEdge[i0] # 最终的边数组
print('edge:\n', edge)
E = 3 # 每个三角形有 3 条边
NE = edge.shape[0] # 获得网格中边的个数, 即 `edge` 的行数
i1 = np.zeros(NE, dtype=np.int32) # 分配空间
i1[j] = range(3 * NC) # totalEdge0 的行数是 3*NC, j 的长度也是 3*NC
print('i0:\n', i0)
print('i1:\n', i1)
edge2cell = np.zeros((NE, 4), dtype=np.int32)
edge2cell[:, 0] = i0 // E # 得到每条边的左边单元
edge2cell[:, 1] = i1 // E # 得到每条边的右边单元
edge2cell[:, 2] = i0 % E # 得到每条边的在左边单元中的局部编号
edge2cell[:, 3] = i1 % E # 得到每条边在其右边单元中的局部编号
print('edge2cell:\n', edge2cell)
mesh = TriangleMesh(node, cell)
mesh.print()
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
mesh.find_edge(axes, showindex=True)
plt.savefig('numpy-mesh-edge.png')
plt.show()
node = mesh.entity('node')
cell = mesh.entity('cell')
print('cell', cell.shape)
bc = mesh.entity_barycenter('cell')
integrator = mesh.integrator(p + 2)
cellmeasure = mesh.entity_measure('cell')
space = LagrangeFiniteElementSpace(mesh, p, spacetype='C')
integralalg = FEMeshIntegralAlg(integrator, mesh)
uI = space.interpolation(lambda x: pde.solution(x, t))
#uI = pde.solution(node,p=node, t=t)
gu = pde.gradient
#uI = space.function()
guI = uI.grad_value
eta = integralalg.L2_error(gu, guI, celltype=True) # size = (cell.shape[0], 2)
eta = np.sum(eta, axis=-1)
print('eta', eta.shape)
tmesh = TriangleMesh(node, cell)
mark = mark(eta, 0.75)
options = tmesh.adaptive_options(method='mean',
maxrefine=10,
maxcoarsen=0,
theta=0.5)
adaptmesh = tmesh.adaptive(eta, options)
#node = adaptmesh.node
fig = plt.figure()
axes = fig.gca()
tmesh.add_plot(axes)
plt.show()
def refine_triangle_rbTest(self, l, plot=True, rb=True):
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.uniform_refine()
mesh = HalfEdgeMesh.from_mesh(mesh)
mesh.ds.cell2hedge = np.array([0, 3, 2, 11, 10])
c = np.array([0.2, 0.2])
r = 1.2
h = 1e-2
k = 0
NB = 0
start = time.time()
while k < l:
halfedge = mesh.ds.halfedge
halfedge1 = halfedge[:, 3]
node = mesh.node
flag = node - c
flag = flag[:, 0]**2 + flag[:, 1]**2
flag = flag <= r**2
flag1 = flag[halfedge[:, 0]].astype(int)
flag2 = flag[halfedge[halfedge1, 0]].astype(int)
markedge = flag1 + flag2 == 1
markedcell = halfedge[markedge, 1]
markedcell = np.unique(markedcell)
cell = np.unique(halfedge[:, 1])
nc = cell.shape[0]
markedcell1 = np.zeros(nc)
markedcell1[markedcell] = 1
if rb:
mesh.refine_triangle_rb(markedcell1)
else:
mesh.refine_triangle_rbg(markedcell1)
k += 1
print('循环', k, '次***************************')
#print('node', node)
#print('cell',cell)
end = time.time()
print(end - start)
if plot:
fig = plt.figure()
axes = fig.gca()
nindex = mesh.nodedata['level']
mesh.add_plot(axes)
#mesh.add_halfedge_plot(axes, showindex=True)
#mesh.find_node(axes, showindex=True, multiindex=nindex)
plt.show()
if 0:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
cindex = np.arange(mesh.number_of_cells() - 1) + 1
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True, multiindex=cindex)
NN = mesh.number_of_nodes()
nindex = np.zeros(NN, dtype=np.int)
halfedge = mesh.ds.halfedge
nindex = mesh.nodedata['level']
cindex = mesh.get_data('cell', 'level')
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True, multiindex=nindex)
mesh.find_cell(axes, showindex=True, multiindex=cindex)
plt.show()
def refine_tri(self, maxit=2, method='rg', plot=True, rb=True):
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)
if False:
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh.from_mesh(mesh)
mesh.ds.cell2hedge = np.array([0, 3, 2, 11, 10])
isMarkedCell = np.array([0, 1, 0, 0, 1], dtype=np.bool_)
#mesh.refine_triangle_rbg(isMarkedCell)
mesh.ds.NV = 3
cell = mesh.ds.cell_to_node()
node = mesh.entity('node')
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
if False:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
if method == 'rg':
color[[4, 13, 17, 28]] = 1
color[[23, 27]] = 2
color[[22, 26]] = 3
mesh.hedgecolor = color
isMarkedCell = np.array(
[0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], dtype=np.bool_)
mesh.refine_triangle_rg(isMarkedCell)
else:
color[[2, 3, 10, 11]] = 1
mesh.hedgecolor = color
isMarkedCell = np.array([0, 1, 1, 0, 0], dtype=np.bool_)
#isMarkedCell = np.array([0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ,0],
# dtype=np.bool_)
mesh.refine_triangle_nvb(isMarkedCell)
mesh.print()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.add_halfedge_plot(axes, showindex=True)
mesh.find_node(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
if True:
mesh = TriangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.init_level_info()
NE = mesh.ds.NE
color = np.zeros(NE * 2, dtype=np.int_)
if method == 'nvb':
color[[2, 3, 10, 11]] = 1
mesh.hedgecolor = color
c = np.array([0.8, 0.8])
r = 0.9
h = 1e-2
k = 0
NB = 0
start = time.time()
while k < maxit:
halfedge = mesh.ds.halfedge
halfedge1 = halfedge[:, 3]
node = mesh.node
flag = node - c
flag = flag[:, 0]**2 + flag[:, 1]**2
flag = flag <= r**2
flag1 = flag[halfedge[:, 0]].astype(int)
flag2 = flag[halfedge[halfedge1, 0]].astype(int)
markedge = flag1 + flag2 == 1
markedcell = halfedge[markedge, 1]
markedcell = np.unique(markedcell)
cell = np.unique(halfedge[:, 1])
nc = cell.shape[0]
markedcell1 = np.zeros(nc)
markedcell1[markedcell] = 1
if method == 'rg':
mesh.refine_triangle_rg(markedcell1.astype(np.bool_))
else:
mesh.refine_triangle_nvb(markedcell1.astype(np.bool_))
k += 1
print('循环', k, '次***************************')
end = time.time()
print('用时', end - start)
if plot:
fig = plt.figure()
axes = fig.gca()
nindex = mesh.nodedata['level']
mesh.add_plot(axes)
#mesh.add_halfedge_plot(axes, showindex=True)
#mesh.find_node(axes, showindex=True, multiindex=nindex)
#mesh.find_cell(axes, showindex=True)
#print(np.c_[np.arange(len(mesh.hedgecolor)), mesh.hedgecolor])
plt.show()
def test_interpolation_plane(self):
def u(p):
x = p[..., 0]
y = p[..., 1]
return x * y
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)
node = mesh.entity('node')
cell = mesh.entity('cell')
tritree = Tritree(node, cell)
mesh = tritree.to_conformmesh()
space = LagrangeFiniteElementSpace(mesh, p=2)
uI = space.interpolation(u)
error0 = space.integralalg.L2_error(u, uI)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, node=space.interpolation_points(), showindex=True)
data = tritree.interpolation(uI)
options = tritree.adaptive_options(method='numrefine',
data={"q": data},
maxrefine=1,
p=2)
if 1:
#eta = space.integralalg.integral(lambda x : uI.grad_value(x)**2, celltype=True, barycenter=True)
#eta = eta.sum(axis=-1)
eta = np.array([1, 0], dtype=np.int)
tritree.adaptive(eta, options)
else:
tritree.uniform_refine(options=options)
fig = plt.figure()
axes = fig.gca()
tritree.add_plot(axes)
tritree.find_node(axes, showindex=True)
mesh = tritree.to_conformmesh(options)
space = LagrangeFiniteElementSpace(mesh, p=2)
data = options['data']['q']
uh = space.to_function(data)
error1 = space.integralalg.L2_error(u, uh)
data = tritree.interpolation(uh)
isLeafCell = tritree.is_leaf_cell()
fig = plt.figure()
axes = fig.gca()
tritree.add_plot(axes)
tritree.find_node(axes,
node=space.interpolation_points(),
showindex=True)
tritree.find_cell(axes, index=isLeafCell, showindex=True)
options = tritree.adaptive_options(method='numrefine',
data={"q": data},
maxrefine=1,
maxcoarsen=1,
p=2)
if 1:
#eta = space.integralalg.integral(lambda x : uI.grad_value(x)**2, celltype=True, barycenter=True)
#eta = eta.sum(axis=-1)
eta = np.array([-1, -1, -1, -1, 0, 1], dtype=np.int)
tritree.adaptive(eta, options)
else:
tritree.uniform_refine(options=options)
mesh = tritree.to_conformmesh(options)
space = LagrangeFiniteElementSpace(mesh, p=2)
data = options['data']['q']
uh = space.to_function(data)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, node=space.interpolation_points(), showindex=True)
mesh.find_cell(axes, showindex=True)
error2 = space.integralalg.L2_error(u, uh)
print(error0)
print(error1)
print(error2)
plt.show()
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)
mesh0.add_plot(axes)
mesh1.add_plot(axes)
plt.show()
dtype=np.float)
cell = np.array([[0, 1, 2, 6], [0, 5, 1, 6], [0, 4, 5, 6], [0, 7, 4, 6],
[0, 3, 7, 6], [0, 2, 3, 6]],
dtype=np.int)
mesh = TetrahedronMesh(point, cell)
mesh.uniform_refine(3)
face = mesh.entity('face')
isBdFace = mesh.ds.boundary_face_flag()
cell = face[isBdFace]
node = mesh.entity('node')
NN = mesh.number_of_nodes()
isBDNode = mesh.ds.boundary_node_flag()
NB = np.sum(isBDNode)
idxmap = np.zeros(NN, dtype=np.int32)
idxmap[isBDNode] = range(NB)
cell = idxmap[cell]
node = node[isBDNode]
trimesh = TriangleMesh(node, cell)
data = {'node': trimesh.node, 'elem': trimesh.ds.cell + 1}
sio.matlab.savemat('trimesh', data)
ax0 = a3.Axes3D(pl.figure())
trimesh.add_plot(ax0)
pl.show()
h = 0.05 mesh_info = MeshInfo() # Set the vertices of the domain [0, 1]^2 mesh_info.set_points([(0, 0), (1, 0), (1, 1), (0, 1)]) # Set the facets of the domain [0, 1]^2 mesh_info.set_facets([[0, 1], [1, 2], [2, 3], [3, 0]]) # Generate the tet mesh mesh = build(mesh_info, max_volume=(h)**2) node = np.array(mesh.points, dtype=np.float) cell = np.array(mesh.elements, dtype=np.int) tmesh = TriangleMesh(node, cell) quality = TriRadiusRatioQuality(tmesh) x0 = quality.get_init_value() R = minimize(quality, x0, method='Powell', callback=quality.callback) print(R) fig = plt.figure() axes = fig.gca() tmesh.add_plot(axes, cellcolor='w') quality.update_mesh_node(R.x) fig = plt.figure() axes = fig.gca() tmesh.add_plot(axes, cellcolor='w') plt.show()
ps = mesh.bc_to_point(bcs).reshape(-1, 2)
val = space.basis(bcs) # (NQ, 1, ldof)
val = space.grad_basis(bcs) # (NQ, NC, ldof, GD)
val = val[:, 0, 0]
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, node=ps, markersize=20)
fig = plt.figure()
axes = fig.add_subplot(projection='3d')
axes.plot_trisurf(ps[:, 0],
ps[:, 1],
val,
linewidth=0.2,
antialiased=True,
cmap='rainbow')
NN = mesh.number_of_nodes()
node = np.zeros((NN, 3), dtype=np.float64)
node[:, 0:2] = mesh.entity('node')
cell = mesh.entity('cell')
mesh3 = TriangleMesh(node, cell)
mesh3.add_plot(axes, box=[0, 1, 0, 1, -1, 1], showaxis=True)
plt.show()
(1, 2, 0),
(3, 0, 2)], dtype=np.int)
mesh = TriangleMesh(node, cell)
mesh.uniform_refine(4)
node = mesh.entity('node')
cell = mesh.entity('cell')
tmesh = Tritree(node, cell)
femspace = LagrangeFiniteElementSpace(mesh, p=1)
uI = femspace.interpolation(f1)
estimator = Estimator(uI[:], mesh, 0.3, 0.5)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes, cellcolor=estimator.eta, showcolorbar=True)
tmesh.adaptive_refine(estimator)
mesh = estimator.mesh
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes, cellcolor=estimator.eta, showcolorbar=True)
femspace = LagrangeFiniteElementSpace(mesh, p=1)
uI = femspace.interpolation(f2)
estimator = Estimator(uI[:], mesh, 0.3, 0.5)
tmesh.adaptive_coarsen(estimator)
mesh = estimator.mesh
fig = plt.figure()
