> El 5 dic 2019, a las 15:12, Manav Bhatia <[email protected]> escribió:
>
> Thanks!
>
> Does the purify option only changes the eigenvector without influencing the
> eigenvalue?
Yes.
>
> -Manav
>
>> On Dec 5, 2019, at 1:54 AM, Jose E. Roman <[email protected]> wrote:
>>
>> In symmetric problems (GHEP) you might have large residuals due to B being
>> singular. The explanation is the following. By default, in SLEPc GHEPs are
>> solved via a B-Lanczos recurrence, that is, using the inner product induced
>> by B. If B is singular this is not a true inner product and numerical
>> problems may arise, in particular, the computed eigenvectors may be
>> corrupted with components in the null space of B. This is easily solved by a
>> small computation called 'eigenvector purification' which is on by default
>> in SLEPc, see EPSSetPurify(). This is described with a bit more detail in
>> section 3.4.4 of the manual.
>>
>> In non-symmetric problems (GNHEP) you should not see this problem. The only
>> precaution is not to solve systems with matrix B, e.g., using
>> shift-and-invert.
>>
>> Jose
>>
>>
>>> El 5 dic 2019, a las 5:04, Manav Bhatia <[email protected]> escribió:
>>>
>>> Hi,
>>>
>>> I am working on mixed form finite element discretization which leads to
>>> eigenvalues of the form
>>>
>>> A x = lambda B x
>>>
>>> With the matrices defined in a block structure as
>>>
>>> A = [ K D^T ]
>>> [ D 0 ]
>>>
>>> B = [ M 0 ]
>>> [ 0 0 ]
>>>
>>> The second row of equations come from Lagrange multipliers in our
>>> discretization scheme. A system with m Lagrange multiplier is expected to
>>> have m Inf eigenvalues. We are testing the standard eigensolvers in Matlab
>>> and as the system size increases the eigensolves are stopping with larger
>>> residuals, || r_i ||, of the eigensystem:
>>>
>>> r_i = A x_i - lambda_i B x_i
>>>
>>> I am working towards setting this up in SLEPc. In the meantime I am curious
>>> about the following:
>>>
>>> 1. Is the eigensolution of such systems known to be problematic?
>>> 2. Are there standard tricks in SLEPc or elsewhere that are geared towards
>>> more robust solutions of such systems?
>>>
>>> I would appreciate guidance on this.
>>>
>>> Regards,
>>> Manav
>>>
>>>
>>
>
