Question

我正在建立一个解决FEniCS项目中PDE的程序，我陷入了组装变分问题的困境。这是导致问题的代码的一部分：

from dolfin import*
import numpy as np
import scipy as sc

mm = 1e-3
Dx = 100 * mm
Dy = 100 * mm
l = 2.1 * mm
e = 1.97 * mm

cond_x = 6.8e-8
cond_y = 9.9e-8

mesh = BoxMesh (-Dx/2.,-Dy/2.,-l,Dx/2,Dy/2,-l-e,10,10,2)

# Create mesh functions for c00, c01, c11, c22
c00 = MeshFunction("double", mesh, 3)
c01 = MeshFunction("double", mesh, 3)
c11 = MeshFunction("double", mesh, 3)
c22 = MeshFunction("double", mesh, 3)

for cell in cells(mesh):
    if (-Dx/2. < cell.midpoint().x() < Dx/2.) and \
       (-Dy/2. < cell.midpoint().y() < Dy/2.) and \
       (-l-e < cell.midpoint().z() < -l):
        c00[cell] = cond_x
        c01[cell] = 0.0
        c11[cell] = cond_y
        c22[cell] = cond_y

# Code for C++ evaluation of conductivity
conductivity_code = """
class Conductivity : public Expression
{
public:

  // Create expression with 4 components
  Conductivity() : Expression(4) {}

  // Function for evaluating expression on each cell
  void eval(Array<double>& values, const Array<double>& x, const ufc::cell& cell) const
  {
    const uint D = cell.topological_dimension;
    const uint cell_index = cell.index;
    values[0] = (*c00)[cell_index];
    values[1] = (*c01)[cell_index];
    values[2] = (*c11)[cell_index];
    values[3] = (*c22)[cell_index];
  }

  // The data stored in mesh functions
  std::shared_ptr<MeshFunction<double> > c00;
  std::shared_ptr<MeshFunction<double> > c01;
  std::shared_ptr<MeshFunction<double> > c11;
  std::shared_ptr<MeshFunction<double> > c22;

};
"""

c = Expression(cppcode=conductivity_code)
c.c00 = c00
c.c01 = c01
c.c11 = c11
c.c22 = c22
C = as_tensor(((c[0], c[1], c[1]), \
               (c[1], c[2], c[1]), \
               (c[1], c[1], c[3])))

# Define function spaces
V = VectorFunctionSpace(mesh, "CG", 1)
Q = FunctionSpace(mesh, "CG", 1)
W = MixedFunctionSpace([V, Q])

(u_r, p_r) = TrialFunctions(W)
(v_r, q_r) = TestFunctions(W)

a_r = inner(C*div(u_r) , div(v_r))*dx

A = assemble(a_r)

当我执行时，我得到以下错误：

Shape mismatch.

Traceback (most recent call last):
  File "/home/chaouki/Documents/Exemples_FEniCS/exe01_ask_a_q.py", line 77, in <module>
    a_r = inner(C*div(u_r) , div(v_r))*dx
  File "/usr/lib/python2.7/dist-packages/ufl/operators.py", line 130, in inner
    return Inner(a, b)
  File "/usr/lib/python2.7/dist-packages/ufl/tensoralgebra.py", line 156, in __new__
    ufl_assert(ash == bsh, "Shape mismatch.")
  File "/usr/lib/python2.7/dist-packages/ufl/assertions.py", line 37, in ufl_assert
    if not condition: error(*message)
  File "/usr/lib/python2.7/dist-packages/ufl/log.py", line 151, in error
    raise self._exception_type(self._format_raw(*message))
UFLException: Shape mismatch.

我不明白错误信息的含义。我该怎么办？

在FEniCS项目中构建解决PDE的程序

0 个答案: