Python PDE Examples

Example #1

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()

Example #2

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()

Example #3

File: PoissonFEMWithRobinBC_example.py Project: zweien/fealpy

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()

Example #4

File: PoissonDGRate2d.py Project: yoczhang/FEALPyExamples

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

Example #5

File: PoissonQBFEMRate.py Project: carlosal1015/fealpy

#!/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