[Trilinos-Users] Matrix Free operator, and loss of accuracy error

[Tom Goffrey]

Hello,

We currently utilise AztecOO GMRES (with condition number estimate) to
solve the linear system resulting from the time implicit solution of
multi-dimensional hydrodynamics. However we have run into problems when
adapting our code to apply a Jacobian free approach.

We replaced our previous explicit Jacobian operator with the matrix free
operator from the NOX package.
(
http://trilinos.org/docs/dev/packages/nox/doc/html/classNOX_1_1Epetra_1_1MatrixFree.html
)

However we find a high proportion of our GMRES solves abort prematurely due
to an error relating to an apparent loss of accuracy:

        Warning: recursive residual indicates convergence
        though the true residual is too large.

        Sometimes this occurs when storage is overwritten (e.g. the
        solution vector was not dimensioned large enough to hold
        external variables). Other times, this is due to roundoff. In
        this case, the solution has either converged to the accuracy
        of the machine or intermediate roundoff errors occurred
        preventing full convergence. In the latter case, try solving
        again using the new solution as an initial guess.

I didn't manage to find much within Trilinos documentation on this, but
from looking through the source code it appears this is triggered by a
significant difference between the recursive residual and the true
residual, where the true residual is calculated for the solution vector,
but the recursive residual is calculated by using an incremental solution
vector.

Currently we believe the high frequency of this error we see for the JFNK
approach is because we have in fact used a non-linear operator (in this
case our non-linear residual function) to approximate the linear
Jacobian-vector product. As such it is not clear to us that this sort of
error checking makes sense in this situation, or perhaps it should be
interpreted as a sign the Jacobian free approximation is becoming worse?

Presumably I can control this error checking by allowing the two residuals
to vary by a greater amount, but I was wondering if others have had similar
problems, and had any advice on the issue?

Of course, any alternative explanation of the high frequency would be
equally appreciated!

Thanks,

Tom Goffrey
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