Unsupported operand type(s) for *: 'Product' and 'Form'

variational formulation
1

I want to use Nitsche’s method to solve stationary NS eqaution.However,I encounter a wierd problem.

Here is my code.

from dolfin import *
from dolfin_adjoint import *
import moola
import matplotlib.pyplot as plt
...
import meshio
geometry = meshio.read("glacier_data/mesh.msh")
meshio.write("glacier_data/mesh.xdmf", meshio.Mesh(points=geometry.points[:,:2], cells={"triangle": geometry.cells["triangle"]}))
meshio.write("glacier_data/mf.xdmf", meshio.Mesh(points=geometry.points[:,:2], cells={"line": geometry.cells["line"]},
                                    cell_data={"line": {"name_to_read": geometry.cell_data["line"]["gmsh:physical"]}}))

mesh = Mesh()
with XDMFFile("glacier_data/mesh.xdmf") as infile:
    infile.read(mesh)
mvc = MeshValueCollection("size_t", mesh, 1)
with XDMFFile("glacier_data/mf.xdmf") as infile:
    infile.read(mvc, "name_to_read")
boundary_markers =MeshFunction("size_t",mesh, mvc)

# Define function spaces (P2-P1)
V = VectorElement("CG", mesh.ufl_cell(), 2)
Q = FiniteElement("CG", mesh.ufl_cell(), 1)
TH = V * Q
W = FunctionSpace(mesh, TH)

# Define test and solution functions
v, q = TestFunctions(W)
s = Function(W,name='State')
u, p = split(s)
f = Function(W.sub(0).collapse(),name="control")

# Set parameter values
nu = Constant(1)      #Viscosity coefficient
gamma=Constant(10)    #Nitsche penalty parameter
n=FacetNormal(mesh)
h=CellVolume(mesh)

# Define boundary conditions
noslip  = DirichletBC(W.sub(0), (0, 0), boundary_markers,2)
inflow  = DirichletBC(W.sub(0), f, boundary_markers,0)
outflow = DirichletBC(W.sub(0), f, boundary_markers,1)

bcs=[inflow,outflow,noslip]
ds=Measure('ds',domain=mesh,subdomain_data=boundary_markers)

# Define the variational formulation of the Navier-Stokes equations
a=nu*inner(grad(u),grad(v))*dx+inner(grad(u)*u,v)*dx-nu*inner(grad(u)*n,v)*ds(2)+\
    inner(p*n,v)*dx-p*div(v)*dx-q*div(u)*dx-nu*inner(grad(v)*n,u)*ds(0)-nu*inner(grad(v)*n,u)*ds(1)+\
    gamma/h*nu*(inner(u,v)*ds(0)+inner(u,v)*ds(1))+\
    inner(q*n,u)*ds(0)+inner(q*n,u)*ds(1)
L=-nu*inner(grad(v)*n,f)*ds(0)-nu*inner(grad(v)*n,f)*ds(1)+gamma/h*nu*inner(f,v)*ds(0)+gamma/h*nu*inner(f,v)*ds(1)+\
    inner(q*n,f)*ds(0)+inner(q*n,f)*ds(1)
solve(a==L,s,bcs)

#moola optimization
...

Error

/usr/bin/python3.6 /home/rsrg/PycharmProjects/glacier_velocity/start_1.py
Traceback (most recent call last):
  File "/home/rsrg/PycharmProjects/glacier_velocity/start_1.py", line 85, in <module>
    inner(q*n,u)*ds(0)+inner(q*n,u)*ds(1)
TypeError: unsupported operand type(s) for *: 'Product' and 'Form'

Process finished with exit code 1
2

There are multiple issues with your code.

You cannot use FacetNormals with volume measure dx.

This should be written as:

    +gamma/h*nu*inner(u,v)*(ds(0)+ds(1))

I have not run the rest of your code, as you do not supply a minimal working example.
Please follow the guidelines in: Read before posting: How do I get my question answered? - #3

4

The main problem is that when you are posting your example with custom data input, there is no way for other people to run your code without alot of modifications from their side. This makes it less likely that you will receive any help. I have already pointed out two issues with your code, as I modified your code to the following:

from dolfin import *

mesh = UnitSquareMesh(10,10)


# Define function spaces (P2-P1)
V = VectorElement("CG", mesh.ufl_cell(), 2)
Q = FiniteElement("CG", mesh.ufl_cell(), 1)
TH = V * Q
W = FunctionSpace(mesh, TH)

# Define test and solution functions
v, q = TestFunctions(W)
s = Function(W,name='State')
u, p = split(s)

# Set parameter values
nu = Constant(1)      #Viscosity coefficient
gamma=Constant(10)    #Nitsche penalty parameter
n=FacetNormal(mesh)
h=CellVolume(mesh)

ds=Measure('ds',domain=mesh)
a=nu*inner(grad(u),grad(v))*dx+inner(grad(u)*u,v)*dx\
   -nu*inner(grad(u)*n,v)*ds(2)\
   +inner(p*n,v)*dx-p*div(v)*dx\
   -q*div(u)*dx-nu*inner(grad(v)*n,u)*ds(0)\
   -nu*inner(grad(v)*n,u)*ds(1)\
   +gamma/h*nu*(inner(u,v)*ds(0)+inner(u,v)*ds(1))\
   +inner(q*n,u)*ds(0)+inner(q*n,u)*ds(1)

In this code, there is no import of dolfin-adjoint, as there is no optimal control specific routines called by the time you get an error message.

This code is a standalone code that anyone can run and reproduce your error message with, and it contains way less code, as no boundary conditions are needed to produce the error message.
Please use this code as a guideline for further questions.

This example can of course be stripped of many more lines, by remove line by line of a, until you are left with the line

which is the one causing the issue.

5

Okay ,I got it.
Thank you very mush.