def test_poisson_fem_2d():
degree = 1
dim = 2
nrefine = 4
maxit = 4
from fealpy.pde.poisson_2d import CosCosData as PDE
pde = PDE()
mesh = pde.init_mesh(n=nrefine)
errorMatrix = np.zeros((2, maxit), dtype=np.float64)
NDof = np.zeros(maxit, dtype=np.int64)
for i in range(maxit):
space = LagrangeFiniteElementSpace(mesh, p=degree)
NDof[i] = space.number_of_global_dofs()
bc = DirichletBC(space, pde.dirichlet)
uh = space.function()
A = space.stiff_matrix()
F = space.source_vector(pde.source)
A, F = bc.apply(A, F, uh)
uh[:] = spsolve(A, F).reshape(-1)
errorMatrix[0, i] = space.integralalg.L2_error(pde.solution, uh)
errorMatrix[1, i] = space.integralalg.L2_error(pde.gradient, uh.grad_value)
if i < maxit-1:
mesh.uniform_refine()
def test_poisson():
p = 1 # 有限元空间次数, 可以增大 p， 看输出结果的变化
n = 4 # 初始网格加密次数
maxit = 4 # 最大迭代次数
pde = PDE()
mesh = pde.init_mesh(n=n)
errorMatrix = np.zeros((2, maxit), dtype=np.float)
NDof = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
space = LagrangeFiniteElementSpace(mesh, p=p) # 建立有限元空间
NDof[i] = space.number_of_global_dofs() # 有限元空间自由度的个数
bc = DirichletBC(space, pde.dirichlet) # DirichletBC 条件
uh = space.function() # 有限元函数
A = space.stiff_matrix() # 刚度矩阵
F = space.source_vector(pde.source) # 载荷向量
A, F = bc.apply(A, F, uh) # 处理边界条件
uh[:] = spsolve(A, F).reshape(-1) # 稀疏矩阵直接解法器
# ml = pyamg.ruge_stuben_solver(A) # 代数多重网格解法器
# uh[:] = ml.solve(F, tol=1e-12, accel='cg').reshape(-1)
errorMatrix[0, i] = space.integralalg.L2_error(
pde.solution, uh
) # 计算 L2 误差
errorMatrix[1, i] = space.integralalg.L2_error(
pde.gradient, uh.grad_value
) # 计算 H1 误差
if i < maxit - 1:
mesh.uniform_refine() # 一致加密网格
assert (errorMatrix < 1.0).all()
from fealpy.functionspace import LagrangeFiniteElementSpace
from fealpy.boundarycondition import RobinBC
from fealpy.tools.show import showmultirate
p = int(sys.argv[1])
n = int(sys.argv[2])
maxit = int(sys.argv[3])
d = int(sys.argv[4])
if d == 2:
from fealpy.pde.poisson_2d import CosCosData as PDE
elif d == 3:
from fealpy.pde.poisson_3d import CosCosCosData as PDE
pde = PDE()
mesh = pde.init_mesh(n=n)
errorType = [
'$|| u - u_h||_{\Omega,0}$', '$||\\nabla u - \\nabla u_h||_{\Omega, 0}$'
]
errorMatrix = np.zeros((2, maxit), dtype=np.float)
NDof = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
space = LagrangeFiniteElementSpace(mesh, p=p)
NDof[i] = space.number_of_global_dofs()
uh = space.function()
A = space.stiff_matrix()
from fealpy.pde.poisson_2d import CosCosData as PDE import numpy as np from ShowCls import ShowCls from PoissonDGModel2d import PoissonDGModel2d from fealpy.mesh import MeshFactory as mf from fealpy.mesh import HalfEdgeMesh2d # from fealpy.mesh.mesh_tools import find_entity # import matplotlib.pyplot as plt # --- begin setting --- # d = 2 # the dimension p = 1 # the polynomial order n = 1 # the number of refine mesh maxit = 5 # the max iteration of the mesh pde = PDE() # create pde model pde.epsilon = -1 # setting the DG-scheme parameter # # epsilon may take -1, 0, 1, # # the corresponding DG-scheme is called symmetric interior penalty Galerkin (SIPG), # # incomplete interior penalty Galerkin (IIPG) and nonsymmetric interior penalty Galerkin (NIPG) pde.eta = 16 # setting the penalty parameter # # To get the optimal rate, one should choose the appropriate 'eta' # # according to the polynomial order 'p', 'epsilon' and mesh. # # error settings 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) # the array to store the number of dofs
#!/usr/bin/env python3
#
import sys
import numpy as np
import matplotlib.pyplot as plt
import scipy.io as sio
# 导入 Poisson 有限元模型
from fealpy.fem.PoissonQBFEMModel import PoissonQBFEMModel
from fealpy.tools.show import showmultirate, show_error_table
from fealpy.pde.poisson_2d import CosCosData as PDE
n = 3
maxit = 4
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, meshtype='quad')
for i in range(maxit):
fem = PoissonQBFEMModel(pde, mesh, q=3) # 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