[petsc-users] Eigensolution with matrices from mixed formulation problems

Manav Bhatia bhatiamanav at gmail.com
Wed Dec 4 22:04:26 CST 2019


   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. 


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