def __init__(self, model, mesh, interval, N):
super(HeatEquationSolver, self).__init__(interval)
self.model = model
self.dt = (interval[1] - interval[0])/N
V = function_space(mesh, 'Lagrange', 1)
uh = FiniteElementFunction(V)
uh[:] = model.init_value(V.interpolation_points())
self.solution = [uh]
self.BC = DirichletBC(V, model.dirichlet, model.is_dirichlet_boundary)
self.stiff_matrix = LaplaceSymetricForm(V, 3).get_matrix()
self.mass_matrix = MassForm(V, 3).get_matrix()
def __init__(self, model, mesh, initTime, stopTime, N, method='FM'):
super(HeatEquationSolver, self).__init__(initTime, stopTime)
self.model = model
self.N = N
self.dt = (stopTime - initTime)/N
self.method = method
self.V = function_space(mesh, 'Lagrange', 1)
uh = FiniteElementFunction(self.V)
uh[:] = model.init_value(self.V.interpolation_points())
self.solution = [uh]
self.maxError = 0.0
self.stiffMatrix = LaplaceSymetricForm(self.V, 3).get_matrix()
self.massMatrix = MassForm(self.V, 3).get_matrix()
from fealpy.model.poisson_model_2d import CosCosData
degree = int(sys.argv[1])
qt = int(sys.argv[2])
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)
degree = int(sys.argv[1])
point = np.array([[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0], [0, 0, 1],
[1, 0, 1], [1, 1, 1], [0, 1, 1]],
dtype=np.float)
cell = np.array([[0, 1, 2, 3, 4, 5, 6, 7]], dtype=np.int)
tree = Octree(point, cell)
tree.uniform_refine()
isLeafCell = tree.is_leaf_cell()
print('child', tree.child)
print('isLeafCell', isLeafCell)
mesh = HexahedronMesh(tree.point, tree.ds.cell[isLeafCell])
V = function_space(mesh, 'Q', degree)
cell2dof = V.cell_to_dof()
ipoints = V.interpolation_points()
ax0 = a3.Axes3D(pl.figure())
ax1 = a3.Axes3D(pl.figure())
mesh.add_plot(ax0)
mesh.find_point(ax0, showindex=True)
mesh.add_plot(ax1)
mesh.find_point(ax1, point=ipoints, showindex=True)
mesh.print()
print('cell2dof:\n', cell2dof)
pl.show()
N = mesh.number_of_points()
I = spdiags(np.ones(N, dtype=np.float), 0, N, N)
P = np.zeros((N, n-1), dtype=np.float)
for i in range(1, n):
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