def interpolation(self, n=2, plot=True):
from fealpy.pde.poisson_2d import CosCosData
from fealpy.functionspace import ConformingVirtualElementSpace2d
pde = CosCosData()
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1)], dtype=np.float64)
cell = np.array([(0, 1, 2, 3)], dtype=np.int_)
mesh = QuadrangleMesh(node, cell)
#mesh = PolygonMesh.from_mesh(mesh)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.uniform_refine(n=n)
#mesh.print()
space = ConformingVirtualElementSpace2d(mesh, p=1)
uI = space.interpolation(pde.solution)
up = space.project_to_smspace(uI)
error = space.integralalg.L2_error(pde.solution, up)
print(error)
if plot:
fig = plt.figure()
axes = fig.gca()
#mesh.add_halfedge_plot(axes, showindex=True)
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 Lshapetest(self, plot=True):
node = np.array([
(-1.0, -1.0),
(0.0, -1.0),
(1.0, -1.0),
(1.0, 0.0),
(0.0, 0.0),
(0.0, 1.0),
(-1.0, 1.0),
(-1.0,0.0)], dtype=np.float)
cell = np.array([[0, 1, 4, 7],[1,2,3,4],[7,4,5,6]], dtype=np.int)
mesh = QuadrangleMesh(node, cell)
mesh.uniform_refine(n=2)
#mesh.node = mesh.node[np.lexsort(mesh.node[:,::-1].T)]
'''
l = len(mesh.node)
node1 = np.zeros((l,2))
node1[:9,:] = mesh.node[mesh.node[:,1] = -1]
node1[9:18,:] = mesh.node[mesh.node[:,1] = -1]
'''
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.node = mesh.node[np.lexsort(mesh.node[:,::-1].T)]
mesh.find_node(axes,showindex = True)
#mesh.find_edge(axes)
#mesh.print()
plt.show()
def refine_RB_test(self, plot=True):
node = np.array([
(0.0, 0.0),
(1.0, 0.0),
(1.0, 1.0),
(0.0, 1.0)], dtype=np.float)
cell = np.array([[0, 1, 2, 3]], dtype=np.int)
mesh = QuadrangleMesh(node, cell)
mesh.uniform_refine()
markedCell = np.array([3], dtype=np.int)
mesh.refine_RB(markedCell)
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)
mesh.print()
plt.show()
def halfedgemesh(n=4, h=4):
"""
半边数据结构的网格
"""
node = np.array([(0, 0), (h, 0), (h, h), (0, h)], dtype=np.float64)
cell = np.array([(0, 1, 2, 3)], dtype=np.int_)
mesh = QuadrangleMesh(node, cell)
mesh = HalfEdgeMesh2d.from_mesh(mesh)
mesh.uniform_refine(n)
return mesh
def test_quadrangle_mesh():
from fealpy.mesh import QuadrangleMesh
node = np.array(
[
(0.0, 0.0), # 0 号点
(0.0, 1.0), # 1 号点
(0.0, 2.0), # 2 号点
(1.0, 0.0), # 3 号点
(1.0, 1.0), # 4 号点
(1.0, 2.0), # 5 号点
(2.0, 0.0), # 6 号点
(2.0, 1.0), # 7 号点
(2.0, 2.0), # 8 号点
],
dtype=np.float64)
cell = np.array(
[
(0, 3, 4, 1), # 0 号单元
(1, 4, 5, 3), # 1 号单元
(3, 6, 7, 4), # 2 号单元
(4, 7, 8, 5), # 3 号单元
],
dtype=np.int_)
mesh = QuadrangleMesh(node, cell)
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()
scale=1)
axes.quiver(space.ccenter[:, 0],
space.ccenter[:, 1],
A0[:, 0],
A0[:, 1],
angles='xy',
scale_units='xy',
scale=1)
plt.show()
node = np.array([(0, 0), (1, 0), (1, 1), (0, 1), (0.5, 0), (1, 0.4), (0.3, 1),
(0, 0.6), (0.5, 0.45)],
dtype=np.float)
cell = np.array([(0, 4, 8, 7), (4, 1, 5, 8), (7, 8, 6, 3), (8, 5, 2, 6)],
dtype=np.int)
pde = CosCosData()
mesh = QuadrangleMesh(node, cell)
mesh.uniform_refine(7)
space = QuadBilinearFiniteElementSpace(mesh)
uI = space.interpolation(pde.solution)
L2 = space.integralalg.L2_error(pde.solution, uI.value)
print("L2:", L2)
H1 = space.integralalg.L2_error(pde.gradient, uI.grad_value)
print("H1:", H1)
