def poisson_fem_2d_neuman_test(self, p=1):
pde = CosCosData()
mesh = pde.init_mesh(n=2)
for i in range(4):
space = LagrangeFiniteElementSpace(mesh, p=p)
A = space.stiff_matrix()
b = space.source_vector(pde.source)
uh = space.function()
bc = BoundaryCondition(space, neuman=pde.neuman)
bc.apply_neuman_bc(b)
c = space.integral_basis()
AD = bmat([[A, c.reshape(-1, 1)], [c, None]], format='csr')
bb = np.r_[b, 0]
x = spsolve(AD, bb)
uh[:] = x[:-1]
area = np.sum(space.integralalg.cellmeasure)
ubar = space.integralalg.integral(pde.solution,
barycenter=False) / area
def solution(p):
return pde.solution(p) - ubar
error = space.integralalg.L2_error(solution, uh)
print(error)
mesh.uniform_refine()
def poisson_test(self, p=2):
pde = CosCosCosData()
mesh = self.plane_pmesh(n=4)
space = PrismFiniteElementSpace(mesh, p=p)
A = space.stiff_matrix()
b = space.source_vector(pde.source)
bc = BoundaryCondition(space, dirichlet=pde.dirichlet)
uh = space.function()
A, b = bc.apply_dirichlet_bc(A, b, uh)
uh[:] = spsolve(A, b).reshape(-1)
error = space.integralalg.L2_error(pde.solution, uh)
print(error)
def poisson_fem_2d_test(self, p=1):
pde = CosCosData()
mesh = pde.init_mesh(n=3)
for i in range(4):
space = LagrangeFiniteElementSpace(mesh, p=p)
A = space.stiff_matrix()
b = space.source_vector(pde.source)
uh = space.function()
bc = BoundaryCondition(space, dirichlet=pde.dirichlet)
A, b = bc.apply_dirichlet_bc(A, b, uh)
uh[:] = spsolve(A, b).reshape(-1)
error = space.integralalg.L2_error(pde.solution, uh)
print(error)
mesh.uniform_refine()
def solve_poisson_robin(self, p=1, n=1, plot=True):
pde = CosCosCosData()
mesh = pde.init_mesh(n=n)
space = LagrangeFiniteElementSpace(mesh, p=p)
A = space.stiff_matrix()
F = space.source_vector(pde.source)
uh = space.function()
bc = BoundaryCondition(space, robin=pde.robin)
A, b = space.set_robin_bc(A, F, pde.robin)
uh[:] = spsolve(A, b).reshape(-1)
error = space.integralalg.L2_error(pde.solution, uh)
print(error)
import numpy as np
from scipy.sparse.linalg import spsolve
import matplotlib.pyplot as plt
from fealpy.pde.linear_elasticity_model import HuangModel2d
from fealpy.functionspace import LagrangeFiniteElementSpace
from fealpy.boundarycondition import BoundaryCondition
p = int(sys.argv[1])
n = int(sys.argv[2])
pde = HuangModel2d(lam=100000, mu=1.0)
mu = pde.mu
lam = pde.lam
mesh = pde.init_mesh(n=n)
space = LagrangeFiniteElementSpace(mesh, p=p)
bc = BoundaryCondition(space, dirichlet=pde.dirichlet)
uh = space.function(dim=2)
#A = space.linear_elasticity_matrix(mu, lam)
A = space.recovery_linear_elasticity_matrix(mu, lam)
F = space.source_vector(pde.source, dim=2)
A, F = bc.apply_dirichlet_bc(A,
F,
uh,
is_dirichlet_boundary=pde.is_dirichlet_boundary)
uh.T.flat[:] = spsolve(A, F)
error = space.integralalg.L2_error(pde.displacement, uh)
print(error)
from fealpy.pde.poisson_2d import CosCosData
from fealpy.functionspace import LagrangeFiniteElementSpace
from fealpy.boundarycondition import BoundaryCondition
pde = CosCosData()
print('test')
mesh = pde.init_mesh(n=7, meshtype='tri')
print('test')
space = LagrangeFiniteElementSpace(mesh, p=1)
print('test')
A = space.stiff_matrix()
print('test')
b = space.source_vector(pde.source)
print('test')
uh = space.function()
bc = BoundaryCondition(space, robin=pde.robin)
bc.apply_robin_bc(A, b)
uh[:] = spsolve(A, b).reshape(-1)
error = space.integralalg.L2_error(pde.solution, uh)
print(error)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
plt.show()
n = int(sys.argv[1])
p = int(sys.argv[2])
scale = float(sys.argv[3])
E = 1e+5
nu = 0.3
pde = LShapeDomainData2d(E=E, nu=nu)
mu = pde.mu
lam = pde.lam
mesh = pde.init_mesh(n=n)
space = LagrangeFiniteElementSpace(mesh, p=p)
bc = BoundaryCondition(space, dirichlet=pde.dirichlet, neuman=pde.neuman)
uh = space.function(dim=2)
A = space.linear_elasticity_matrix(mu, lam)
F = space.source_vector(pde.source, dim=2)
bc.apply_neuman_bc(F, is_neuman_boundary=pde.is_neuman_boundary)
A, F = bc.apply_dirichlet_bc(A,
F,
uh,
is_dirichlet_boundary=pde.is_dirichlet_boundary)
uh.T.flat[:] = spsolve(A, F)
error = space.integralalg.L2_error(pde.displacement, uh)
bc = mesh.entity_barycenter('edge')
maxit = 4
pde = CosCosData()
box = pde.domain()
# # error settings
errorType = [
'$|| u - u_h||_0$', '$||\\nabla u - \\nabla u_h||_E$',
'$||\\nabla u - \\nabla u_h||_E0$', '$||\\nabla u - \\nabla u_h||_1$'
]
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
for i in range(maxit):
mesh = triangle(box, h / 2**(i - 1), meshtype='polygon')
space = ConformingVirtualElementSpace2d(mesh, p=1)
uh = space.function()
bc = BoundaryCondition(space, dirichlet=pde.dirichlet)
A0, S0 = space.chen_stability_term()
A0 = A0.toarray()
S0 = S0.toarray()
A0 = space.stiff_matrix()
F0 = space.source_vector(pde.source)
A, F = bc.apply_dirichlet_bc(A0, F0, uh)
uh[:] = spsolve(A, F)
sh = space.project_to_smspace(uh)
# # L2-error
errorMatrix[0, i] = space.integralalg.L2_error(pde.solution, sh)
def apply_boundary_condition(self, A, b, timeline):
t1 = timeline.next_time_level()
bc = BoundaryCondition(self.space,
neuamn=lambda x: self.pde.neuman(x, t1))
b = bc.apply_neuman_bc(b)
return A, b