def solve_poisson_3d(self, n=2):
from fealpy.pde.poisson_3d import CosCosCosData as PDE
from fealpy.mesh import MeshFactory
from fealpy.functionspace import LagrangeFiniteElementSpace
from fealpy.boundarycondition import DirichletBC
pde = PDE()
mf = MeshFactory()
m = 2**n
box = [0, 1, 0, 1, 0, 1]
mesh = mf.boxmesh3d(box, nx=m, ny=m, nz=m, meshtype='tet')
space = LagrangeFiniteElementSpace(mesh, p=1)
gdof = space.number_of_global_dofs()
NC = mesh.number_of_cells()
print('gdof:', gdof, 'NC:', NC)
bc = DirichletBC(space, pde.dirichlet)
uh = space.function()
A = space.stiff_matrix()
A = space.parallel_stiff_matrix(q=1)
M = space.parallel_mass_matrix(q=2)
M = space.mass_matrix()
F = space.source_vector(pde.source)
A, F = bc.apply(A, F, uh)
solver = PETScSolver()
solver.solve(A, F, uh)
error = space.integralalg.L2_error(pde.solution, uh)
print(error)
def __init__(self):
self.domain = [0, 50, 0, 50]
self.mesh = MeshFactory().regular(self.domain, n=50)
self.timeline = UniformTimeLine(0, 1, 100)
self.space0 = RaviartThomasFiniteElementSpace2d(self.mesh, p=0)
self.space1 = ScaledMonomialSpace2d(self.mesh, p=1) # 线性间断有限元空间
self.vh = self.space0.function() # 速度
self.ph = self.space0.smspace.function() # 压力
self.ch = self.space1.function(dim=3) # 三个组分的摩尔密度
self.options = {
'viscosity': 1.0,
'permeability': 1.0,
'temperature': 397,
'pressure': 50,
'porosity': 0.2,
'injecttion_rate': 0.1,
'compressibility': (0.001, 0.001, 0.001),
'pmv': (1.0, 1.0, 1.0),
'dt': self.timeline.dt
}
c = self.options['viscosity'] / self.options['permeability']
self.A = c * self.space0.mass_matrix()
self.B = self.space0.div_matrix()
phi = self.options['porosity']
self.M = phi / dt * self.space0.smspace.mass_matrix() #
self.MC = self.space1.cell_mass_matrix() / dt
def __init__(self, pde, timeline, n=1):
self.pde = pde
box = pde.domain()
mf = MeshFactory()
self.mesh = mf.boxmesh2d(box, nx=n, ny=n, meshtype='tri')
self.uspace = RaviartThomasFiniteElementSpace2d(self.mesh, p=0)
self.pspace = self.uspace.smspace
self.timeline = timeline
NL = timeline.number_of_time_levels()
# state variable
self.yh = self.pspace.function(dim=NL)
self.uh = self.pspace.function(dim=NL)
self.tph = self.uspace.function(dim=NL)
self.ph = self.uspace.function()
bc = self.mesh.entity_barycenter('cell')
f = cartesian(lambda p: pde.y_solution(p, 0))
self.yh[:, 0] = self.pspace.local_projection(f)
# costate variable
self.zh = self.pspace.function(dim=NL)
self.tqh = self.uspace.function(dim=NL)
self.qh = self.uspace.function()
self.A = self.uspace.stiff_matrix() # RT 质量矩阵
self.D = self.uspace.div_matrix() # (p, \div v)
self.M = self.pspace.mass_matrix()
def show_mesh(self, p=2, plot=True):
mf = MeshFactory()
mesh = mf.boxmesh2d([0, 1, 0, 1], nx=2, ny=2, meshtype='tri')
node = mesh.entity('node')
cell = mesh.entity('cell')
ltmesh = LagrangeTriangleMesh(node, cell, p=p)
NN = ltmesh.number_of_nodes()
mesh.ds.edge = ltmesh.lds.edge
mesh.ds.edge2cell = ltmesh.lds.edge2cell
node = ltmesh.entity('node')
#ltmesh.print()
if plot:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
mesh.find_node(axes, node=node, showindex=True, fontsize=28)
mesh.find_edge(axes, showindex=True)
mesh.find_cell(axes, showindex=True)
plt.show()
def diff_index_test(self, p=3):
mfactory = MeshFactory()
mesh = mfactory.one_tetrahedron_mesh()
space = ScaledMonomialSpace3d(mesh, p=p)
index = space.diff_index_1()
print(index)
index = space.diff_index_2()
print(index)
def space_mesh(self, n=10):
from fealpy.mesh import MeshFactory
mf = MeshFactory()
mesh = mf.boxmesh2d(self.domain, nx=2, ny=2, meshtype='tri')
for i in range(n):
isCrossedCell = mesh.is_crossed_cell(self.point, self.segment)
mesh.bisect(isCrossedCell)
return mesh
def save_mesh(self, p=2, fname='test.vtu'):
mf = MeshFactory()
mesh = mf.boxmesh2d([0, 1, 0, 1], nx=2, ny=2, meshtype='quad')
node = mesh.entity('node')
cell = mesh.entity('cell')
mesh = LagrangeQuadrangleMesh(node, cell[:, [0, 3, 1, 2]], p=p)
mesh.to_vtk(fname=fname)
def one_tet_mesh_test(self, p, plot=True):
mfactory = MeshFactory()
mesh = mfactory.one_tetrahedron_mesh()
space = ScaledMonomialSpace3d(mesh, p=p)
if plot:
fig = plt.figure()
axes = fig.gca(projection='3d')
mesh.add_plot(axes)
axes.set_axis_off()
plt.show()
def space_mesh(self, n=10):
from fealpy.mesh import MeshFactory
mf = MeshFactory()
mesh = mf.boxmesh2d(self.domain, nx=1, ny=1, meshtype='tri')
point = self.fracture['point']
segment = self.fracture['segment']
for i in range(n):
isCutCell = mesh.find_segment_location(point, segment)
mesh.bisect(isCutCell)
return mesh
def space_mesh(self, n=50):
"""
Notes
-----
最小网格单元尺寸为 1 m
"""
box = [0, 50, 0, 50]
mf = MeshFactory()
mesh = mf.boxmesh2d(box, nx=n, ny=n, meshtype='tri')
return mesh
def space_mesh(self, p, NS=0):
from fealpy.mesh import MeshFactory
mf = MeshFactory()
mesh = mf.boxmesh2d(self.domain, nx=70, ny=30, p=p, meshtype='quad')
mesh.uniform_refine(NS)
return mesh
def __init__(self):
self.mf = MeshFactory()
def space_mesh(self, n=32):
from fealpy.mesh import MeshFactory
mf = MeshFactory()
mesh = mf.boxmesh2d(self.domain, nx=n, ny=n, meshtype='tri')
return mesh
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()
M = space.mass_matrix()
def init_mesh(self):
d = self.domain()
mfactory = MeshFactory()
mesh = mfactory.regular(d)
return mesh
def space_mesh(self, n=50):
box = [0, 50, 0, 50]
mf = MeshFactory()
mesh = mf.boxmesh2d(box, nx=n, ny=n, meshtype='tri')
return mesh