theta = 0.2
k = maxit - 15
p = 1
q = 3
errorType = ['$|| u_I - u_h ||_{l_2}$',
'$|| u - u_h||_{0}$',
'$||\\nabla u - \\nabla u_h||_{0}$',
'$||\\nabla u - G(\\nabla u_h)||_{0}$']
ralg = FEMFunctionRecoveryAlg()
Ndof = np.zeros((maxit,), dtype=np.int)
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
for i in range(maxit):
print('step:', i)
fem = PoissonFEMModel(pde, mesh, 1, q=3)
fem.solve()
uh = fem.uh
Ndof[i] = fem.mesh.number_of_nodes()
errorMatrix[0, i] = fem.l2_error()
errorMatrix[1, i] = fem.L2_error()
errorMatrix[2, i] = fem.H1_semi_error()
# rguh = ralg.harmonic_average(uh)
# eta = fem.recover_estimate(rguh)
eta = fem.residual_estimate()
errorMatrix[3, i] = np.sqrt(np.sum(eta**2))
markedCell = mark(eta, theta=theta)
if i < maxit - 1:
isMarkedCell = mark(eta, theta=theta)
A = mesh.bisect(isMarkedCell, returnim=True)
errorType = ['$|| u_I - u_h ||_{l_2}$',
'$|| u - u_h||_{0}$',
'$||\\nabla u - \\nabla u_h||_{0}$',
'$||\\nabla u - G(\\nabla u_h)||_{0}sim$',]
maxit = 1
ralg = FEMFunctionRecoveryAlg()
Ndof = np.zeros((maxit,), dtype=np.int)
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
integrator = mesh.integrator(3)
for i in range(maxit):
print('step:', i)
fem = PoissonFEMModel(pde, mesh, 1, integrator)
fem.solve()
uh = fem.uh
Ndof[i] = fem.mesh.number_of_nodes()
errorMatrix[0, i] = fem.get_l2_error()
errorMatrix[1, i] = fem.get_L2_error()
errorMatrix[2, i] = fem.get_H1_error()
rguh = ralg.simple_average(uh)
eta = fem.recover_estimate(rguh)
errorMatrix[3, i] = fem.get_recover_error(rguh)
estimator = Estimator(uh[:], mesh, 0.3, 0.5)
tmesh.adaptive_refine(estimator)
if i < maxit - 1:
mesh = estimator.mesh
Ndof = np.zeros((maxit, ), dtype=np.int)
errorType = [
'$|| u - u_h||_0$ with p=1',
'$|| u - u_h||_0$ with p=2',
'$|| u - u_h||_0$ with p=3',
'$||\\nabla u - \\nabla u_h||_0$ with p=1',
'$||\\nabla u - \\nabla u_h||_0$ with p=2',
'$||\\nabla u - \\nabla u_h||_0$ with p=3',
]
ps = [1, 2, 3]
q = [4, 5, 6]
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
for i in range(maxit):
Ndof[i] = mesh.number_of_nodes()
for j, p in enumerate(ps):
integrator = mesh.integrator(q[j])
fem = PoissonFEMModel(pde, mesh, p, integrator)
fem.solve()
Ndof[i] = fem.femspace.number_of_global_dofs()
errorMatrix[j, i] = fem.get_L2_error()
errorMatrix[j + 3, i] = fem.get_H1_error()
if i < maxit - 1:
mesh.uniform_refine()
print(errorMatrix)
showmultirate(plt, 0, Ndof, errorMatrix, errorType)
plt.show()
p = int(sys.argv[2]) # 有限元空间的次数
n = int(sys.argv[3]) # 初始网格的加密次数
maxit = int(sys.argv[4]) # 迭代加密的次数
pde = PDE() # 创建 pde 模型
# 误差类型与误差存储数组
errorType = ['$|| u - u_h||_0$', '$||\\nabla u - \\nabla u_h||_0$']
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
# 自由度数组
Ndof = np.zeros(maxit, dtype=np.int)
# 创建初始网格对象
mesh = pde.init_mesh(n)
for i in range(maxit):
fem = PoissonFEMModel(pde, mesh, p, q=p + 2) # 创建 Poisson 有限元模型
ls = fem.solve() # 求解
Ndof[i] = fem.space.number_of_global_dofs() # 获得空间自由度个数
errorMatrix[0, i] = fem.L2_error() # 计算 L2 误差
errorMatrix[1, i] = fem.H1_semi_error() # 计算 H1 误差
if i < maxit - 1:
mesh.uniform_refine() # 一致加密网格
# 显示误差
show_error_table(Ndof, errorType, errorMatrix)
# 可视化误差收敛阶
showmultirate(plt, 0, Ndof, errorMatrix, errorType)
plt.show()
else:
return False
pde = LShapeRSinData()
mesh = pde.init_mesh(n=4, meshtype='tri')
integrator = mesh.integrator(3)
node = mesh.entity('node')
cell = mesh.entity('cell')
tmesh = Tritree(node, cell)
pmesh = tmesh.to_conformmesh()
tol = 1.0e-4
for i in range(maxit):
fem = PoissonFEMModel(pde, pmesh, p, integrator)
fem.solve()
res = fem.get_H1_error()
#res = fem.get_L2_error()
estimator = Estimator(fem.uh[:], mesh, 0.3, 0.5)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes, cellcolor=estimator.eta, showcolorbar=True)
if res < tol:
break
tmesh.adaptive_refine(estimator)
pmesh = tmesh.to_conformmesh()
print("Steps:", i)
#tmesh.find_node(axes, showindex=True)
plt.show()
p = 1
maxit = 5
pde = PDE()
errorType = ['$|| u - u_h||_0$', '$||\\nabla u - \\nabla u_h||_0$']
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
Ndof = np.zeros(maxit, dtype=np.int)
integrator = tmesh.integrator(7)
for i in range(maxit):
fem = PoissonFEMModel(pde, tmesh, p, integrator)
ls = fem.solve()
sio.savemat('test%d.mat' % (i), ls)
Ndof[i] = fem.femspace.number_of_global_dofs()
errorMatrix[0, i] = fem.get_L2_error()
errorMatrix[1, i] = fem.get_H1_error()
if i < maxit - 1:
#tmesh.uniform_refine()
h = h / 2
pmesh = distmesh2d(fd, h, box, pfix, meshtype='polygon')
node = pmesh.entity('node')
t = Delaunay(node)
tmesh = TriangleMesh(node, t.simplices.copy())
area = tmesh.entity_measure('cell')
tmesh.delete_cell(area < 1e-8)
area = tmesh.entity_measure('cell')
from fealpy.pde.poisson_3d import LShapeRSinData as PDE
p = int(sys.argv[2]) # 有限元空间的次数
n = int(sys.argv[3]) # 初始网格的加密次数
maxit = int(sys.argv[3])
theta = int(sys.argv[4])
pde = PDE() # 创建 pde 模型
mesh = pde.init_mesh(n)
errorType = ['$|| u - u_h||_{0}$', '$||\\nabla u - \\nabla u_h||_{0}$']
Ndof = np.zeros((maxit, ), dtype=np.int)
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
for i in range(maxit):
print('step:', i)
fem = PoissonFEMModel(pde, mesh, p, q=p + 2) # 创建 Poisson 有限元模型
fem.solve() # 求解
uh = fem.uh
space = uh.space
Ndof[i] = space.mesh.number_of_nodes()
errorMatrix[0, i] = fem.L2_error() # 计算 L2 误差
errorMatrix[1, i] = fem.H1_semi_error() # 计算 H1 误差
rguh = space.grad_recovery(uh)
eta = fem.recover_estimate(rguh)
markedCell = mark(eta, theta=theta, method='MAX')
if i < maxit - 1:
markedCell = mark(eta, theta=theta, method='MAX')
mesh.bisect(markedCell)
# 可视化误差收敛阶
p = int(sys.argv[2]) # 有限元空间的次数
n = int(sys.argv[3]) # 初始网格的加密次数
maxit = int(sys.argv[4]) # 迭代加密的次数
pde = PDE() # 创建 pde 模型
# 误差类型与误差存储数组
errorType = ['$|| u - u_h||_0$', '$||\\nabla u - \\nabla u_h||_0$']
errorMatrix = np.zeros((len(errorType), maxit), dtype=np.float)
# 自由度数组
Ndof = np.zeros(maxit, dtype=np.int)
# 创建初始网格对象
mesh = pde.init_mesh(n)
for i in range(maxit):
fem = PoissonFEMModel(pde, mesh, p, p + 2) # 创建 Poisson 有限元模型
ls = fem.solve() # 求解
Ndof[i] = fem.space.number_of_global_dofs() # 获得空间自由度个数
errorMatrix[0, i] = fem.get_L2_error() # 计算 L2 误差
errorMatrix[1, i] = fem.get_H1_error() # 计算 H1 误差
if i < maxit - 1:
mesh.uniform_refine() # 一致加密网格
# 显示误差
show_error_table(Ndof, errorType, errorMatrix)
# 可视化误差收敛阶
showmultirate(plt, 0, Ndof, errorMatrix, errorType)
plt.show()