singular systems, petsc and slepc

[Umut Tabak]

Dear all,

As a fresh user of Petsc libraries, should thank the developers for such 
a magnificent endeavor and years of work.

So the question directly related to Petsc is that if I have a singular 
system matrix and try to solve for the unknowns(simple enough 3 by 3) (I 
am using the simple linear system example from the Petsc user manual as 
a template where a preconditioner is used, I guess it is Jacobi.), I do 
not get any warnings for zero pivots in LU decomposition which I could 
not understand why, and the results are on the order of e+16, also the 
norm of the error. But why is not there some kind of warning.

The second part of the question is related to Slepc, this might not find 
direct answers here perhaps, but let me give it a try.

I have a generalized eigenvalue problem, it is a vibration related 
problem so I will use K and M instead of A and B, respectively. On my 
problem, K is singular, and if I use slepc to find the solution, petsc 
warns me about the zero pivot emergence, and breaks down naturally, 
there after I apply some shift operations that are already implemented 
in slepc to overcome the problem.

The question is what is the effect of preconditioner on a singular 
matrix for the linear system explained above, somehow, I was thinking in 
any case that should also warn me but it did not and gave some wrong 
results.

I am a bit weak on the preconditioners, maybe should have done some 
reading but I know that singular systems can also have solutions by some 
order tricks, pseudo inverse, temporary links application solutions with 
respect to rigid body modes(from structural mechanics too specific maybe).

Can Petsc handle singular systems as well? I am a bit confused at this 
point.

Best regards,

Umut