def diff_index_test(self, p=3):
mfactory = MeshFactory()
mesh = mfactory.one_tetrahedron_mesh()
space = ScaledMonomialSpace3d(mesh, p=p)
index = space.diff_index_1()
print(index)
index = space.diff_index_2()
print(index)
def show_frame_test(self):
fig = plt.figure()
axes = fig.gca(projection='3d')
mfactory = MeshFactory()
mesh = mfactory.one_tetrahedron_mesh()
space = ScaledMonomialSpace3d(mesh, p=1)
space.show_frame(axes)
plt.show()
class HalfEdgeMesh3dTest:
def __init__(self):
self.meshfactory = MeshFactory()
def one_tetrahedron_mesh_test(self):
tmesh = self.meshfactory.one_tetrahedron_mesh(ttype='equ')
mesh = HalfEdgeMesh3d.from_mesh(tmesh)
mesh.print()
def one_tet_mesh_test(self, p, plot=True):
mfactory = MeshFactory()
mesh = mfactory.one_tetrahedron_mesh()
space = ScaledMonomialSpace3d(mesh, p=p)
if plot:
fig = plt.figure()
axes = fig.gca(projection='3d')
mesh.add_plot(axes)
axes.set_axis_off()
plt.show()
class RaviartThomasFiniteElementSpace3dTest:
def __init__(self):
self.meshfactory = MeshFactory()
def show_basis_test(self, p=0):
mesh = self.meshfactory.one_tetrahedron_mesh(ttype='equ')
space = RaviartThomasFiniteElementSpace3d(mesh, p=p, q=2)
fig = plt.figure()
space.show_basis(fig)
plt.show()
def cell_basis_test(self):
mfactory = MeshFactory()
mesh = mfactory.one_tetrahedron_mesh(ttype='iso')
space = ScaledMonomialSpace3d(mesh, p=2)
bc = np.array([[1, 0, 0, 0]])
point = mesh.bc_to_point(bc, 'cell')
print(point.shape)
print(space.cellsize)
phi = space.basis(point)
print(phi)
def face_basis_test(self):
mfactory = MeshFactory()
mesh = mfactory.one_tetrahedron_mesh(ttype='iso')
space = ScaledMonomialSpace3d(mesh, p=1)
face = mesh.entity('face')
print(face)
print('frame:', space.faceframe)
bc = np.array([[1 / 3, 1 / 3, 1 / 3]])
bc = np.array([[1, 0, 0]])
point = mesh.bc_to_point(bc, 'face')
print(point.shape)
phi = space.face_basis(point)
print(phi)
class RaviartThomasFiniteElementSpace3dTest:
def __init__(self):
self.meshfactory = MeshFactory()
def show_basis(self, p=0):
mesh = self.meshfactory.one_tetrahedron_mesh(ttype='equ')
space = RaviartThomasFiniteElementSpace3d(mesh, p=p, q=2)
fig = plt.figure()
space.show_basis(fig)
plt.show()
def basis_coefficients(self, n=0, p=0):
pde = X2Y2Z2Data()
mesh = pde.init_mesh(n=n, meshtype='tet')
space = RaviartThomasFiniteElementSpace3d(mesh, p=p)
C = space.basis_coefficients()
return C
def solve_poisson_3d(self, n=0, p=0, plot=True):
pde = CosCosCosData()
mesh = pde.init_mesh(n=n, meshtype='tet')
space = RaviartThomasFiniteElementSpace3d(mesh, p=p, q=p + 4)
udof = space.number_of_global_dofs()
pdof = space.smspace.number_of_global_dofs()
gdof = udof + pdof
uh = space.function()
print('uh:', uh.shape)
ph = space.smspace.function()
print('ph:', ph.shape)
A = space.stiff_matrix()
B = space.div_matrix()
F1 = space.source_vector(pde.source)
AA = bmat([[A, -B], [-B.T, None]], format='csr')
F0 = space.neumann_boundary_vector(pde.dirichlet)
FF = np.r_['0', F0, F1]
x = spsolve(AA, FF).reshape(-1)
uh[:] = x[:udof]
ph[:] = x[udof:]
error0 = space.integralalg.L2_error(pde.flux, uh)
def f(bc):
xx = mesh.bc_to_point(bc)
return (pde.solution(xx) - ph(xx))**2
error1 = space.integralalg.integral(f)
print(error0, error1)
def show_face_basis_index_test(self):
mfactory = MeshFactory()
mesh = mfactory.one_tetrahedron_mesh()
space = ScaledMonomialSpace3d(mesh, p=3)
space.show_face_basis_index(p=3)
def face_index_test(self, p=3):
mfactory = MeshFactory()
mesh = mfactory.one_tetrahedron_mesh()
space = ScaledMonomialSpace3d(mesh, p=p)
space.face_diff_index_1()
import numpy as np from fealpy.mesh import MeshFactory import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D mf = MeshFactory() mesh = mf.one_tetrahedron_mesh(meshtype='iso') node = np.array([[0, 0, 0],[0, 1, 0],[1, 0, 0],[0, 0, 1]],dtype=np.float) cell = np.array([0, 1, 2, 3],dtype=np.float) #计算6倍四面体体积 v0 = node[1,:]-node[0,:] v1 = node[2,:]-node[0,:] v2 = node[3,:]-node[0,:] nv = np.cross(v0,-v1) V = np.dot(nv, v2)#四面体的6倍体积 Dlambda = np.zeros((4,3), dtype=np.float) W = np.array([[-1,0,0], [0,1,0], [0,0,-1]], dtype=np.float) node1 = np.array([[1,1,1],node[0:3,1],node[0:3,2]]) node2 = np.array([[1,1,1],node[0:3,0],node[0:3,2]]) node3 = np.array([[1,1,1],node[0:3,0],node[0:3,1]]) a1 = np.linalg.det(node1) a2 = np.linalg.det(node2) a3 = np.linalg.det(node3) Dlambda[0,:] = [a1,a2,a3]@W/V node4 = np.array([[1,1,1],node[1:4,1],node[1:4,2]]) node5 = np.array([[1,1,1],node[1:4,0],node[1:4,2]]) node6 = np.array([[1,1,1],node[1:4,0],node[1:4,1]]) a4 = np.linalg.det(node4) a5 = np.linalg.det(node5) a6 = np.linalg.det(node6)