def get_current_linear_system(self):
V = self.V
model = self.model
t = self.currentTime
S = self.stiffMatrix
M = self.massMatrix
k = model.diffusion_coefficient()
bc = DirichletBC(self.V, lambda p: model.dirichlet(p, t), model.is_dirichlet_boundary)
F = SourceForm(V, lambda p: model.source(p, t), 3).get_vector()
dt = self.dt
if self.method is 'FM':
b = dt*(F - k*[email protected][-1]) + [email protected][-1]
A, b = bc.apply(M, b)
return A, b
if self.method is 'BM':
b = dt*F + [email protected][-1]
A = M + dt*k*S
A, b = bc.apply(A, b)
return A, b
if self.method is 'CN':
b = dt*F + (M - 0.5*dt*k*S)@self.solution[-1]
A = M + 0.5*dt*k*S
A, b = bc.apply(A, b)
return A, b
n = int(sys.argv[3])
box = [0, 1, 0, 1]
model = CosCosData()
mesh = rectangledomainmesh(box, nx=n, ny=n, meshtype='tri')
maxit = 4
Ndof = np.zeros(maxit, dtype=np.int)
error = np.zeros(maxit, dtype=np.float)
ratio = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
V = function_space(mesh, 'Lagrange', degree)
uh = FiniteElementFunction(V)
Ndof[i] = V.number_of_global_dofs()
a = LaplaceSymetricForm(V, qt)
L = SourceForm(V, model.source, qt)
bc = DirichletBC(V, model.dirichlet, model.is_boundary)
point = V.interpolation_points()
solve(a, L, uh, dirichlet=bc, solver='direct')
error[i] = L2_error(model.solution, uh, order=qt)
# error[i] = np.sqrt(np.sum((uh - model.solution(point))**2)/Ndof[i])
if i < maxit-1:
mesh.uniform_refine()
# 输出结果
ratio[1:] = error[0:-1]/error[1:]
print('Ndof:', Ndof)
print('error:', error)
print('ratio:', ratio)
#fig = plt.figure()
P[:, i-1] = sinsin(i, point)
return bmat([[I, P]])
box = [0, 1, 0, 1]
n = 6
model = CosCosData()
mesh = rectangledomainmesh(box, nx=2**n, ny=2**n, meshtype='tri')
N = mesh.number_of_points()
V = function_space(mesh, 'Lagrange', 1)
point = V.interpolation_points()
uh = FiniteElementFunction(V)
a = LaplaceSymetricForm(V, 3)
L = SourceForm(V, model.source, 3)
bc = DirichletBC(V, model.dirichlet, model.is_boundary)
A = a.get_matrix()
b = L.get_vector()
A, b = bc.apply(A, b)
PI = prolongate_matrix(mesh, n)
AA = PI.transpose()@A@PI
bb = PI.transpose()@b
DL = tril(AA).tocsc()
DLInv = inv(DL)
U = triu(AA, 1)
x0 = np.zeros(N+n-1, dtype=np.float)
from fealpy.mesh.simple_mesh_generator import rectangledomainmesh
from fealpy.functionspace.tools import function_space
from fealpy.form.Form import LaplaceSymetricForm, MassForm, SourceForm
from fealpy.boundarycondition import DirichletBC
from fealpy.erroranalysis import L2_error
from fealpy.functionspace.function import FiniteElementFunction
model = SinCosExpData()
box = [0, 1, 0, 1]
n = 10
mesh = rectangledomainmesh(box, nx=n, ny=n, meshtype='tri')
V = function_space(mesh, 'Lagrange', 1)
Ndof = V.number_of_global_dofs()
A = LaplaceSymetricForm(V, 3).get_matrix()
M = MassForm(V, 3).get_matrix()
b = SourceForm(V, model.source, 1).get_vector()
BC = DirichletBC(V, model.dirichlet, model.is_dirichlet_boundary)
T0 = 0.0
T1 = 1
N = 400
dt = (T1 - T0) / N
print(dt)
uh = FiniteElementFunction(V)
uh[:] = model.init_value(V.interpolation_points())
uht = [uh]
MD = BC.apply_on_matrix(M)
for i in range(1, N + 1):
t = T0 + i * dt