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[Christian Clason <question149919@xxxxxxxxxxxxxxxxxxxxx>]

New question #149919 on DOLFIN:
https://answers.launchpad.net/dolfin/+question/149919

I am trying to solve a nonlinear pde-constrained optimization problem with a reduced Newton method, where instead of constructing the full Hessian, I compute the action of the Hessian on a function for use in a Krylov solver such as CG. 

I assume that this can be done by constructing a PETScKrylovMatrix and defining a suitable mult function. (If there is a more high-level way of doing this, I'd be grateful for a hint.) However, I'm a bit stumped by the interface between PETSc and Dolfin here. The core step in the matrix multiplication would be something like

def mult(self, *args) :  
    du = Function(V,args[0])
    L = du*v*dx
    problem = VariationalProblem(a, L, bc)
    y = problem.solve()
    args[1] = y.vector()

(assume that the function space V, test function v, boundary conditions bc and bilinear form a have all been defined previously). This however doesn't work, since args[0] and args[1] are not of proper type. How do I need to massage args[0] and args[1] to make this work? Any hints would be appreciated, especially a template for the use of PETScKrylovMatrix in Python.

(If I can get this working, I'd be happy to turn this into a documented demo. I'm sure there are more people interested in using FEniCS as a framework for pde-constrained optimization.)

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