Norm of residuum

Question

Hi,
I have a nonlinear problem defined in the following way

    self.mesh = dolfin.Mesh(meshXML);
    V = FunctionSpace(self.mesh, 'Lagrange', self.lagrangeSpaceDim)
    bc = boundary_definition()
    du = TrialFunction(V)
    u_ = Function(V)     # most recently computed solution
    u_ = self.solveLinearOn(V, bc)#interpolate(Expression("x[0]"), V)
    #could not call u_ = self.solveLinear(meshXML, lagrangeSpaceDim) this problem described here
    #http://fenicsproject.org/qa/3537/mesh-xml-inconsistent-import
    v  = TestFunction(V)
    F  = inner(self.psi(sqrt(2)*sqrt(inner(nabla_grad(u_), nabla_grad(u_))))*nabla_grad(u_), nabla_grad(v))*dx
    J  = derivative(F, u_, du)  # Gateaux derivative in dir. of du

    #could not do problem = NonlinearVariationalProblem(F, u_, bc.fullBC(V), J) probably due to pointer misimplementation
    bcs = bc.fullBC(V)
    problem = NonlinearVariationalProblem(F, u_, bcs, J)

so that u_ is a initial guess solution. Then I basically call

solver  = NonlinearVariationalSolver(problem)
solver.solve()
return(u_)

I would like for particular object u_ (which I import from elsewhere or solve by another program) to know residual norm of the F. So basically norm of the vector of F applied on each test function, which is called residual norm. Is there some way to do that?

I found that NonlinearVariationalProblem has member residual_form(). But I do not know how extract the information about its particullar value for the set of test functions.

Answer 1

Have you tried to assemble F? I was successful doing that once, but I am afraid I deleted the code and do not recall exactly how I did it. I do know you have to be careful applying the boundary conditions.

Comments

Thank you. For me worked this pseudo code which I am posting here for inspiration. I figured out finally how to get rid of Dirichlet boundary conditions data.

bcs = bc.fullBC(V)
problem = NonlinearVariationalProblem(F, u_, bcs, J)
x = problem.residual_form()
indicators = assemble(x)
if type(bcs) is list:
    for i in range(0, len(bcs)):
        bcs[i].apply(indicators, u_.vector())#hack for Dirichlet boundary conditions
    else:
        bcs.apply(indicators, u_.vector())
error = numpy.linalg.norm(indicators.array())
plot(Function(V, indicators))