def test_poisson_equation(self, p=1, maxit=4):
h = 0.1
pde = CosCosData()
domain = pde.domain()
error = np.zeros((maxit,), dtype=np.float)
for i in range(maxit):
mesh = triangle(domain, h, meshtype='polygon')
dmodel = SobolevEquationWGModel2d(self.pde, mesh, p=p)
uh = dmodel.space.function()
dmodel.space.set_dirichlet_bc(uh, pde.dirichlet)
S = dmodel.space.stabilizer_matrix()
A = dmodel.G + S
F = dmodel.space.source_vector(pde.source)
F -= A@uh
isBdDof = dmodel.space.boundary_dof()
gdof = dmodel.space.number_of_global_dofs()
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] = uh[isBdDof]
uh[:] = spsolve(A, F)
integralalg = dmodel.space.integralalg
error[i] = integralalg.L2_error(pde.solution, uh)
h /= 2
print(error)
print(error[0:-1]/error[1:])
from scipy.sparse import csr_matrix
import sys
import sympy
from mpl_toolkits.mplot3d import Axes3D
from fealpy.decorator import cartesian
from scipy.sparse.linalg import spsolve
from fealpy.boundarycondition import DirichletBC
from fealpy.pde.poisson_2d import CosCosData as PDE
from fealpy.tools.show import showmultirate, show_error_table
n = 10
p = 4
mf = MeshFactory()
mesh = mf.boxmesh2d([0, 1, 0, 1], nx=n, ny=n, meshtype='tri')
pde = PDE()
domain = pde.domain()
maxit = 4
errorType = [
'$|| u - u_h||_{\Omega,0}$', # L2 误差
'$||\\nabla u - \\nabla u_h||_{\Omega, 0}$'
] # H1 误差
errorMatrix = np.zeros((2, maxit), dtype=np.float)
NDof = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
print('Step:', i)
space = LagrangeFiniteElementSpace(mesh, p=p)
NDof[i] = space.number_of_global_dofs()
uh = space.function()
a = np.array([(10.0, -1.0), (-1.0, 2.0)], dtype=np.float64)
A = space.stiff_matrix(c=a)
A0, S0 = space.chen_stability_term()
A = space.stiff_matrix()
print("A:", A.toarray())
print("A0:", A0.toarray())
print("S0:", S0.toarray())
np.savetxt('A.txt', A.toarray(), fmt='%.2e')
np.savetxt('A0.txt', A0.toarray(), fmt='%.2e')
np.savetxt('S0.txt', S0.toarray(), fmt='%.2e')
if False:
h = 0.1
maxit = 1
pde = CosCosData()
box = pde.domain()
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()
A = space.stiff_matrix()
F = space.source_vector(pde.source)
A, F = bc.apply_dirichlet_bc(A, F, uh)
from fealpy.pde.poisson_2d import CosCosData
from fealpy.mesh import MeshFactory
from fealpy.decorator import cartesian, barycentric
from fealpy.functionspace import RaviartThomasFiniteElementSpace2d
from fealpy.solver import SaddlePointFastSolver
p = int(sys.argv[1]) # RT 空间的次数
n = int(sys.argv[2]) # 初始网格部分段数
maxit = int(sys.argv[3]) # 迭代求解次数
pde = CosCosData() # pde 模型
box = pde.domain() # 模型区域
mf = MeshFactory() # 网格工场
for i in range(maxit):
mesh = mf.boxmesh2d(box, nx=n, ny=n, meshtype='tri')
space = RaviartThomasFiniteElementSpace2d(mesh, p=p)
udof = space.number_of_global_dofs()
pdof = space.smspace.number_of_global_dofs()
gdof = udof + pdof
print("step ", i, " with number of dofs:", gdof)
uh = space.function()
ph = space.smspace.function()