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