[petsc-users] Solving Ill Conditioned Problems

[Nachiket Gokhale]

On Thu, Oct 18, 2012 at 2:28 PM, Matthew Knepley <knepley at gmail.com> wrote:
> On Thu, Oct 18, 2012 at 11:07 AM, Nachiket Gokhale <gokhalen at gmail.com>
> wrote:
>>
>> Hi,
>>
>> I am solving a Piezoelectric problem using Petsc. The structure is
>>
>> [ K_uu        K_uv ]
>> [K_uv ^T   -K_v,v ]
>>
>> More details about the formulation:  http://tinyurl.com/9hlbp4u
>>
>> K_uu  has elements O(1E9)  because the stiffnesses are in GPa,
>> K_uv   has elements O(1) because piezoelectric coefficients are of that
>> order
>> K_v,v  has  elements O(1E-9) because the dielectric constants are of
>> that order.
>>
>> I am using Petsc, with pc_type LU and MUMPS for the factorization,
>> -ksp_type gmres. I am not sure if my solution is converging. A typical
>> solve seems to be doing this:
>>
>> 28 KSP preconditioned resid norm 5.642364260456e-06 true resid norm
>> 1.228976487745e-03 ||r(i)||/||b|| 3.317409023627e-14
>>  29 KSP preconditioned resid norm 5.540718271043e-06 true resid norm
>> 1.228453548651e-03 ||r(i)||/||b|| 3.315997440178e-14
>>  30 KSP preconditioned resid norm 1.973052106578e-03 true resid norm
>> 1.220399172500e-03 ||r(i)||/||b|| 3.294256047735e-14
>>  31 KSP preconditioned resid norm 1.155762663956e-17 true resid norm
>> 2.447631111938e-04 ||r(i)||/||b|| 6.606955965570e-15
>>
>> Is there a right way to solve this set of equations? Is PCFieldSplit
>> the recommended way?
>
>
> First, you should really non-dimensionalize. You can see what this would
> give
> you by symmetrically scaling your problem with [ 3e4 3e-4 ], namely
> everything
> will be O(1).
>
> Second, you might get something out of using FieldSplit, but its tough to
> tell
> without knowing more about the operators.
>
>    Matt
>
>>
>> Thanks,
>>
>> -Nachiket
>

Oh, right, thanks. I wasn't even thinking of it that way. I'll scale
the variables and I'll give it a try.

Cheers,

-Nachiket



>
>
>
> --
> What most experimenters take for granted before they begin their experiments
> is infinitely more interesting than any results to which their experiments
> lead.
> -- Norbert Wiener