Questions about ArityMismatch: Adding expressions with non-matching form arguments ('v_1',) vs ()-

General
1

I want to assemble the bilinear form res and linear formLwith the boundaries composed of 5 parts. The definition of the constant functions used in res and L are

f=fem.Constant(domain,PETSc.ScalarType(1))
a=fem.Constant(domain,np.array([1,1],dtype=PETSc.ScalarType))
kappa=fem.Constant(domain,PETSc.ScalarType(1e-3))
boundary_zero=fem.Constant(domain,PETSc.ScalarType(0))
boundary_one=fem.Constant(domain,PETSc.ScalarType(1))

and the definition of res and L are

res_Galerkin=dot(a,grad(u))*v*dx+kappa*dot(grad(u),grad(v))*dx+(-div(grad(u))*kappa+dot(a,grad(u))-f)*dot(coeff*a,grad(v))*h*dx
res_boundary=-dot(a,n)*u*v*ds(1)-dot(a,n)*u*v*ds(2)-dot(a,n)*u*v*ds(3)-kappa*dot(grad(u),n)*v*ds(1)-kappa*dot(grad(u),n)*v*ds(2)-kappa*dot(grad(u),n)*v*ds(3)-kappa*dot(grad(u),n)*v*ds(4)-kappa*dot(grad(u),n)*v*ds(5)+u*dot(kappa*grad(v),n)*ds(1)+u*dot(kappa*grad(v),n)*ds(2)+u*dot(kappa*grad(v),n)*ds(3)+u*dot(kappa*grad(v),n)*ds(4)+u*dot(kappa*grad(v),n)*ds(5)+beta/h*u*kappa*v*ds(1)+beta/h*u*kappa*v*ds(2)+beta/h*u*kappa*v*ds(3)+beta/h*u*kappa*v*ds(4)+beta/h*u*kappa*v*ds(5)
res=res_Galerkin+res_boundary

L=(f*v*dx+f*dot(coeff*a,grad(v))*h*dx
   -dot(a,n)*boundary_one*v*ds(1)
   +boundary_one*dot(kappa*grad(v),n)*ds(1)+beta/h*boundary_one*kappa*v*ds(1))

where n is the facet normal.
I put the res and L into LinearProblem() and try to solve this problem and I catch the following error

ArityMismatch: Adding expressions with non-matching form arguments ('v_1',) vs ().

But when I try to use res1=lhs(res+L) and L1=rhs(res+L) and solve the problem, it is right.
So I want to know where is wrong with my original assembling? Thanks in advance!

The boundaries are defined as

boundaries=[(1,lambda x:np.logical_and(np.isclose(x[0],0),np.logical_and(x[1]>0.3-1e-10,x[1]<=1))),
            (2,lambda x:np.logical_and(np.isclose(x[0],0),np.logical_and(x[1]<0.3+1e-10,x[1]>=0))),
            (3,lambda x:np.isclose(x[1],0)),
            (4,lambda x:np.isclose(x[0],1)),
            (5,lambda x:np.isclose(x[1],1))]
facet_indices,facet_markers=[],[]
fdim=domain.topology.dim-1
for (marker,locator) in boundaries:
    facets=mesh.locate_entities(domain,fdim,locator)
    facet_indices.append(facets)
    facet_markers.append(np.full_like(facets,marker))
facets_indices=np.hstack(facet_indices).astype(np.int32)
facets_markers=np.hstack(facet_markers).astype(np.int32)
sorted_facets=np.argsort(facets_indices)
facet_tag=mesh.meshtags(domain,fdim,facets_indices[sorted_facets],facets_markers[sorted_facets])
2

Dear @Discoverer ,
the snippets you present are not sufficient to reproduce your error message, please make sure that you define all variables that one would need to reproduce the error message.

Also as your problem is

try calling dolfinx.fem.form(res) and dolfinx.fem.form(L), and remove term by term from your variational form until you know what term causes the error message.

3

Really thanks. I find where I am wrong.
Can I ask for another question about : here I define ds=Measure('ds',domain=domain,subdomain_data=facet_tag)
so if I want to integrate on all of the boundary, can I still use something like f*v*ds?

4

Yes, you can do that.

5

Thank you very much.