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[Christian Clason <question150334@xxxxxxxxxxxxxxxxxxxxx>]

New question #150334 on DOLFIN:
https://answers.launchpad.net/dolfin/+question/150334

Now that PETScKrylovSolver can be called from Python for KrylovMatrix, I've hit another snag: In some cases, PETScKrylovSolver returns the right hand side vector after one iteration. Curiously, "monitor_convergence" claims that the preconditioned residual is zero, although there is no preconditioner (and the true residual is given correctly). Below is a code with a working and a non-working example. Am I overlooking something? Again, any hint would be appreciated.

Christian

###

from dolfin import *

def boundary(x,on_boundary):
    return on_boundary

mesh = UnitSquare(32, 32)
V = FunctionSpace(mesh, 'CG', 1)

bc = DirichletBC(V, Constant(0.0), boundary)
u = TrialFunction(V); v = TestFunction(V)
A, b = assemble_system( inner(grad(u), grad(v))*dx, Constant(1.0)*v*dx, bc)

class NewtonMatrix(PETScKrylovMatrix) :
    def __init__(self) :
        PETScKrylovMatrix.__init__(self, V.dim(), V.dim())

    def mult(self, *args) :  
        x = args[0]; bc.apply(x)
        solve(A,args[1],x)

class NewtonMatrix2(PETScKrylovMatrix) :
    def __init__(self) :
        PETScKrylovMatrix.__init__(self, V.dim(), V.dim())

    def mult(self, *args) :  
        x = args[0]; 
        y = A*x
        args[1][:] = y[:]


NewtonSolver = PETScKrylovSolver('cg', 'none')
NewtonSolver.parameters["monitor_convergence"] = True

y = Function(V)
solve(A,y.vector(),b)

x_petsc = PETScVector(V.dim())

print NewtonSolver.solve(NewtonMatrix(), x_petsc, down_cast(y.vector())) # twenty iterations
print (b - x_petsc).norm('l2') # works: this is zero 

x_petsc.zero()

print NewtonSolver.solve(NewtonMatrix2(), x_petsc, down_cast(b)) # only one iteration
print (y.vector() - x_petsc).norm('l2') # doesn't work: this is not zero
print (b - x_petsc).norm('l2') # but this is


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