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On 21/09/15 10:38, Justin Chang wrote:
> Hello again,
>
> I am still having issues with this, what I had done originally was
> not correct.
>
> In FEniCS, all I had to do was
>
> A_D, b_D = assemble_system(a_D, L_D, bcs_D)
>
> And feed the A_D and b_D terms into scipy's optimization.
> Essentially I am solving:
>
> min 0.5*x^T*A_D*x - x^T*b_D
>
> and the gradient of the above would be:
>
> A_D*x - b_D
>
> I have attached said FEniCS code (named "Decay_Problem_3.py") which
> solves a different problem, but the concept is the same.
>
> However, this methodology does not work with my current setup. If
> I replicate the above in Firedrake, the entire solution seems to be
> fixated to the dirichlet BCs and whatever initial conditions I have
> provided, which I am guessing is what you were warning me about
> previously. Do you guys handle Dirichlet boundary conditions
> differently than how FEniCS handles theirs? I have also attached my
> current firedrake code (named "2D_plume_ADR_ex1.py", the parts in
> question begin at line 161)

Ah, OK.  So when you assemble an operator with boundary conditions,
the bc rows /and/ columns are zeroed and a 1 is placed on the
diagonal.  The appropriate RHS for this linear is system is then not
just the linear form L_D assembled with the bcs applied.  You need to
"lift" the boundary conditions from the operator to the RHS.
assemble_system does this under the hood for you.  I think things will
work if you do the following:

# I assume the solution space is W
A_D = assemble(a_D, bcs=bcs_D)

tmp = Function(W)
for bc in bcs_D:
    bc.apply(tmp)

rhs_bcs = assemble(action(a_D, tmp))

b_D = assemble(L_D)
b_D -= rhs_bcs
for bc in bcs_D:
    bc.apply(b_D)

More details on the background here:

www.firedrakeproject.org/boundary_conditions.html

Cheers,

Lawrence
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