def solve_poisson_3d(self, n=0, p=0, plot=True):
pde = CosCosCosData()
mesh = pde.init_mesh(n=n, meshtype='tet')
space = RaviartThomasFiniteElementSpace3d(mesh, p=p, q=p + 4)
udof = space.number_of_global_dofs()
pdof = space.smspace.number_of_global_dofs()
gdof = udof + pdof
uh = space.function()
print('uh:', uh.shape)
ph = space.smspace.function()
print('ph:', ph.shape)
A = space.stiff_matrix()
B = space.div_matrix()
F1 = space.source_vector(pde.source)
AA = bmat([[A, -B], [-B.T, None]], format='csr')
F0 = space.neumann_boundary_vector(pde.dirichlet)
FF = np.r_['0', F0, F1]
x = spsolve(AA, FF).reshape(-1)
uh[:] = x[:udof]
ph[:] = x[udof:]
error0 = space.integralalg.L2_error(pde.flux, uh)
def f(bc):
xx = mesh.bc_to_point(bc)
return (pde.solution(xx) - ph(xx))**2
error1 = space.integralalg.integral(f)
print(error0, error1)
def basis_coefficients(self, n=0, p=0):
pde = X2Y2Z2Data()
mesh = pde.init_mesh(n=n, meshtype='tet')
space = RaviartThomasFiniteElementSpace3d(mesh, p=p)
C = space.basis_coefficients()
return C
def __init__(self,
vdata,
cdata,
mesh,
timeline,
p=0,
options={
'rdir': '/home/why/result',
'step': 1000,
'porosity': 0.2
}):
self.options = options
self.vdata = vdata
self.cdata = cdata
self.mesh = mesh
self.timeline = timeline
self.uspace = RaviartThomasFiniteElementSpace3d(mesh, p=p)
self.cspace = ScaledMonomialSpace3d(mesh, p=p + 1)
self.uh = self.uspace.function() # 速度场自由度数组
self.ph = self.uspace.smspace.function() # 压力场自由度数组
self.ch = self.cspace.function() # 浓度场自由度数组
# 初始浓度场设为 0
ldof = self.cspace.number_of_local_dofs()
print("cell_mass_matrix:")
self.M = self.cspace.cell_mass_matrix()
self.H = inv(self.M)
self.set_init_velocity_field() # 计算初始的速度场和压力场
# vtk 文件输出
node, cell, cellType, NC = self.mesh.to_vtk()
self.points = vtk.vtkPoints()
self.points.SetData(vnp.numpy_to_vtk(node))
self.cells = vtk.vtkCellArray()
self.cells.SetCells(NC, vnp.numpy_to_vtkIdTypeArray(cell))
self.cellType = cellType
def __init__(self, model, T=800 * 3600 * 24, NS=32, NT=800 * 24):
self.model = model
self.mesh = model.space_mesh(n=NS)
self.timeline = model.time_mesh(T=T, n=NT)
self.GD = model.GD
if self.GD == 2:
self.vspace = RaviartThomasFiniteElementSpace2d(self.mesh,
p=0) # 速度空间
elif self.GD == 3:
self.vspace = RaviartThomasFiniteElementSpace3d(self.mesh, p=0)
self.pspace = self.vspace.smspace # 压强和饱和度所属的空间, 分片常数
self.cspace = LagrangeFiniteElementSpace(self.mesh, p=1) # 位移空间
# 上一时刻物理量的值
self.v = self.vspace.function() # 速度函数
self.p = self.pspace.function() # 压强函数
self.s = self.pspace.function() # 水的饱和度函数 默认为0, 初始时刻区域内水的饱和度为0
self.u = self.cspace.function(dim=self.GD) # 位移函数
self.phi = self.pspace.function() # 孔隙度函数, 分片常数
# 当前时刻物理量的值, 用于保存临时计算出的值, 模型中系数的计算由当前时刻
# 的物理量的值决定
self.cv = self.vspace.function() # 速度函数
self.cp = self.pspace.function() # 压强函数
self.cs = self.pspace.function() # 水的饱和度函数 默认为0, 初始时刻区域内水的饱和度为0
self.cu = self.cspace.function(dim=self.GD) # 位移函数
self.cphi = self.pspace.function() # 孔隙度函数, 分片常数
# 初值
self.p[:] = model.rock['initial pressure'] # MPa
self.phi[:] = model.rock['porosity'] # 初始孔隙度
self.cp[:] = model.rock['initial pressure'] # 初始地层压强
self.cphi[:] = model.rock['porosity'] # 当前孔隙度系数
# 源项, TODO: 注意这里假设用的是结构网格, 换其它的网格需要修改代码
self.fo = self.cspace.function()
self.fo[-1] = -self.model.oil['production rate'] # 产出
self.fw = self.cspace.function()
self.fw[0] = self.model.water['injection rate'] # 注入
# 一些常数矩阵和向量
# 速度散度矩阵, 速度方程对应的散度矩阵, (\nabla\cdot v, w)
self.B = self.vspace.div_matrix()
# 压强方程对应的位移散度矩阵, (\nabla\cdot u, w) 位移散度矩阵
# * 注意这里利用了压强空间分片常数, 线性函数导数也是分片常数的事实
c = self.mesh.entity_measure('cell')
c *= self.model.rock['biot']
val = self.mesh.grad_lambda() # (NC, TD+1, GD)
val *= c[:, None, None]
pc2d = self.pspace.cell_to_dof()
cc2d = self.cspace.cell_to_dof()
pgdof = self.pspace.number_of_global_dofs()
cgdof = self.cspace.number_of_global_dofs()
I = np.broadcast_to(pc2d, shape=cc2d.shape)
J = cc2d
self.PU0 = csr_matrix((val[..., 0].flat, (I.flat, J.flat)),
shape=(pgdof, cgdof))
self.PU1 = csr_matrix((val[..., 1].flat, (I.flat, J.flat)),
shape=(pgdof, cgdof))
if self.GD == 3:
self.PU2 = csr_matrix((val[..., 2].flat, (I.flat, J.flat)),
shape=(pgdof, cgdof))
# 线弹性矩阵的右端向量
sigma0 = self.pspace.function()
sigma0[:] = self.model.rock['initial stress']
self.FU = np.zeros(self.GD * cgdof, dtype=np.float64)
self.FU[0 * cgdof:1 * cgdof] -= self.p @ self.PU0
self.FU[1 * cgdof:2 * cgdof] -= self.p @ self.PU1
if self.GD == 3:
self.FU[2 * cgdof:3 * cgdof] -= self.p @ self.PU2
# 初始应力和等效应力项
self.FU[0 * cgdof:1 * cgdof] -= sigma0 @ self.PU0
self.FU[1 * cgdof:2 * cgdof] -= sigma0 @ self.PU1
if self.GD == 3:
self.FU[2 * cgdof:3 * cgdof] -= sigma0 @ self.PU2
# vtk 文件输出
node, cell, cellType, NC = self.mesh.to_vtk()
self.points = vtk.vtkPoints()
self.points.SetData(vnp.numpy_to_vtk(node))
self.cells = vtk.vtkCellArray()
self.cells.SetCells(NC, vnp.numpy_to_vtkIdTypeArray(cell))
self.cellType = cellType
def show_basis(self, p=0):
mesh = self.meshfactory.one_tetrahedron_mesh(ttype='equ')
space = RaviartThomasFiniteElementSpace3d(mesh, p=p, q=2)
fig = plt.figure()
space.show_basis(fig)
plt.show()
def __init__(self, mesh, args, ctx):
self.ctx = ctx
self.args = args # 模拟相关参数
NT = int((args.T1 - args.T0)/args.DT)
self.timeline = UniformTimeLine(args.T0, args.T1, NT)
self.mesh = mesh
if self.ctx.myid == 0:
self.GD = mesh.geo_dimension()
if self.GD == 2:
self.vspace = RaviartThomasFiniteElementSpace2d(self.mesh, p=0) # 速度空间
elif self.GD == 3:
self.vspace = RaviartThomasFiniteElementSpace3d(self.mesh, p=0)
self.pspace = self.vspace.smspace # 压力和饱和度所属的空间, 分片常数
self.cspace = LagrangeFiniteElementSpace(self.mesh, p=1) # 位移空间
# 上一时刻物理量的值
self.v = self.vspace.function() # 速度函数
self.p = self.pspace.function() # 压力函数
self.s = self.pspace.function() # 水的饱和度函数 默认为0, 初始时刻区域内水的饱和度为0
self.u = self.cspace.function(dim=self.GD) # 位移函数
self.phi = self.pspace.function() # 孔隙度函数, 分片常数
# 当前时刻物理量的值, 用于保存临时计算出的值, 模型中系数的计算由当前时刻
# 的物理量的值决定
self.cv = self.vspace.function() # 速度函数
self.cp = self.pspace.function() # 压力函数
self.cs = self.pspace.function() # 水的饱和度函数 默认为0, 初始时刻区域内水的饱和度为0
self.cu = self.cspace.function(dim=self.GD) # 位移函数
self.cphi = self.pspace.function() # 孔隙度函数, 分片常数
# 初值
self.s[:] = self.mesh.celldata['fluid_0']
self.p[:] = self.mesh.celldata['pressure_0'] # MPa
self.phi[:] = self.mesh.celldata['porosity_0'] # 初始孔隙度
self.s[:] = self.mesh.celldata['fluid_0']
self.cp[:] = self.p # 初始地层压力
self.cphi[:] = self.phi # 当前孔隙度系数
# 源汇项
self.f0 = self.cspace.function()
self.f1 = self.cspace.function()
self.f0[:] = self.mesh.nodedata['source_0'] # 流体 0 的源汇项
self.f1[:] = self.mesh.nodedata['source_1'] # 流体 1 的源汇项
# 一些常数矩阵和向量
# 速度散度矩阵, 速度方程对应的散度矩阵, (\nabla\cdot v, w)
self.B = self.vspace.div_matrix()
# 压力方程对应的位移散度矩阵, (\nabla\cdot u, w) 位移散度矩阵
# * 注意这里利用了压力空间分片常数, 线性函数导数也是分片常数的事实
c = self.mesh.entity_measure('cell')
c *= self.mesh.celldata['biot']
val = self.mesh.grad_lambda() # (NC, TD+1, GD)
val *= c[:, None, None]
pc2d = self.pspace.cell_to_dof()
cc2d = self.cspace.cell_to_dof()
pgdof = self.pspace.number_of_global_dofs()
cgdof = self.cspace.number_of_global_dofs()
I = np.broadcast_to(pc2d, shape=cc2d.shape)
J = cc2d
self.PU0 = csr_matrix(
(val[..., 0].flat, (I.flat, J.flat)),
shape=(pgdof, cgdof)
)
self.PU1 = csr_matrix(
(val[..., 1].flat, (I.flat, J.flat)),
shape=(pgdof, cgdof)
)
if self.GD == 3:
self.PU2 = csr_matrix(
(val[..., 2].flat, (I.flat, J.flat)),
shape=(pgdof, cgdof)
)
# 线弹性矩阵的右端向量
self.FU = np.zeros(self.GD*cgdof, dtype=np.float64)
self.FU[0*cgdof:1*cgdof] -= [email protected]
self.FU[1*cgdof:2*cgdof] -= [email protected]
if self.GD == 3:
self.FU[2*cgdof:3*cgdof] -= [email protected]
# 初始应力和等效应力项
sigma = self.mesh.celldata['stress_0'] + self.mesh.celldata['stress_eff']# 初始应力和等效应力之和
self.FU[0*cgdof:1*cgdof] -= [email protected]
self.FU[1*cgdof:2*cgdof] -= [email protected]
if self.GD == 3:
self.FU[2*cgdof:3*cgdof] -= [email protected]
m = int(sys.argv[1])
n = int(sys.argv[2])
p = int(sys.argv[3])
if m == 0:
pde = CornerData3D()
elif m == 1:
pass
elif m == 2:
pass
elif m == 3:
pass
mesh = pde.init_mesh(n=n, meshtype='tet')
space = RaviartThomasFiniteElementSpace3d(mesh, p=p)
udof = space.number_of_global_dofs()
pdof = space.smspace.number_of_global_dofs()
gdof = udof + pdof + 1
uh = space.function()
ph = space.smspace.function()
A = space.stiff_matrix()
B = space.div_matrix()
C = space.smspace.cell_mass_matrix()[:, 0, :].reshape(-1)
F1 = space.source_vector(pde.source)
AA = bmat([[A, -B, None], [-B.T, None, C[:, None]], [None, C, None]],
format='csr')