def show_basis(self):
h = 0.5
box = [-h, 1 + h, -h, np.sqrt(3) / 2 + h]
mesh = MeshFactory.one_triangle_mesh()
space = FirstKindNedelecFiniteElementSpace2d(mesh, p=0)
fig = plt.figure()
space.show_basis(fig, box=box)
plt.show()
class FirstKindNedelecFiniteElementSpace2dTest:
def __init__(self):
self.meshfactory = MeshFactory()
def show_basis_test(self):
h = 0.5
box = [-h, 1 + h, -h, np.sqrt(3) / 2 + h]
mesh = self.meshfactory.one_triangle_mesh()
space = FirstKindNedelecFiniteElementSpace2d(mesh, p=0, q=2)
fig = plt.figure()
space.show_basis(fig, box=box)
plt.show()
class RaviartThomasFiniteElementSpace2dTest:
def __init__(self):
self.meshfactory = MeshFactory()
def show_basis(self):
h = 0.5
box = [-h, 1+h, -h, np.sqrt(3)/2+h]
mesh = self.meshfactory.one_triangle_mesh('equ')
space = RaviartThomasFiniteElementSpace2d(mesh, p=2, q=2)
fig = plt.figure()
space.show_basis(fig, box=box)
plt.show()
def solve_poisson_2d(self):
pde = CosCosData()
mesh = pde.init_mesh(n=3, methtype='tri')
space = RaviartThomasFiniteElementSpace2d(mesh, p=0)
import numpy as np
import matplotlib.pyplot as plt
from fealpy.mesh.core import multi_index_matrix1d
from fealpy.mesh.core import multi_index_matrix2d
from fealpy.mesh.core import multi_index_matrix3d
from fealpy.mesh import MeshFactory as MF
p = 6
mesh = MF.one_triangle_mesh(meshtype='equ')
mi = multi_index_matrix2d(p) # ((p+1)*(p+2)/2, 3)
print(mi)
bcs = mi / p
ps = mesh.bc_to_point(bcs).reshape(-1, 2)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, showindex=True, fontsize=24)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, node=ps, showindex=True, markersize=100, fontsize=28)
plt.show()
if False:
mi1 = multi_index_matrix1d(p)
print('mi1:\n', mi1 / p)
class FirstKindNedelecFiniteElementSpace2dTest:
def __init__(self):
self.meshfactory = MeshFactory()
def show_basis(self):
h = 0.5
box = [-h, 1 + h, -h, np.sqrt(3) / 2 + h]
mesh = self.meshfactory.one_triangle_mesh()
space = FirstKindNedelecFiniteElementSpace2d(mesh, p=0)
fig = plt.figure()
space.show_basis(fig, box=box)
plt.show()
def interpolation(self, n=4, p=0, plot=True):
box = [-0.5, 1.5, -0.5, 1.5]
def u(p):
x = p[..., 0]
y = p[..., 1]
val = np.zeros_like(p)
pi = np.pi
val[..., 0] = np.sin(pi * x) * np.cos(pi * y)
val[..., 1] = np.sin(pi * x) * np.cos(pi * y)
return val
mesh = self.meshfactory.regular([0, 1, 0, 1], n=n)
space = FirstKindNedelecFiniteElementSpace2d(mesh, p=p)
uI = space.interpolation(u)
error = space.integralalg.L2_error(u, uI)
print(error)
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes, box=box)
plt.show()
def solve_time_harmonic_2d(self, n=3, p=0, plot=True):
pde = CosSinData()
mesh = pde.init_mesh(n=n, meshtype='tri')
space = FirstKindNedelecFiniteElementSpace2d(mesh, p=p)
gdof = space.number_of_global_dofs()
uh = space.function()
A = space.curl_matrix() - space.mass_matrix()
F = space.source_vector(pde.source)
isBdDof = space.boundary_dof()
bdIdx = np.zeros(gdof, dtype=np.int)
bdIdx[isBdDof] = 1
Tbd = spdiags(bdIdx, 0, gdof, gdof)
T = spdiags(1 - bdIdx, 0, gdof, gdof)
A = T @ A @ T + Tbd
F[isBdDof] = 0
uh[:] = spsolve(A, F)
error0 = space.integralalg.L2_error(pde.solution, uh)
error1 = space.integralalg.L2_error(pde.curl, uh.curl_value)
print(error0, error1)
if plot:
box = [-0.5, 1.5, -0.5, 1.5]
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes, box=box)
#mesh.find_node(axes, showindex=True)
#mesh.find_edge(axes, showindex=True)
#mesh.find_cell(axes, showindex=True)
#node = ps.reshape(-1, 2)
#uv = phi.reshape(-1, 2)
#axes.quiver(node[:, 0], node[:, 1], uv[:, 0], uv[:, 1])
plt.show()