Eigen value and eigen vector analysis

[Theodore Omtzigt]

I am researching eigen value/vector algorithms and their uses. I would like to understand the relationship between eigen value/vector usage in circuit simulation and in structural mechanics vibrational analysis. Does anyone know of a good reference or can describe how these analyses are used in practise?

[John Peterson]

Hi,

In the LibMesh library we use SLEPc to solve eigenproblems. SLEPc is based on the PETSc linear algebra library. You can find it online here, and here's a paper reference.

@Article{Hernandez:2005:SSF,
author = "Vicente Hernandez and Jose E. Roman and Vicente Vidal",
title = "{SLEPc}: A Scalable and Flexible Toolkit for the Solution of Eigenvalue Problems",
journal = "ACM Transactions on Mathematical Software",
volume = "31",
number = "3",
pages = "351--362",
month = sep,
year = "2005"
}

I can't comment on your specific applications, but one frequently would like to know not all the eigenvalues of a particular matrix A, but rather the few largest or few smallest eigenvalues. SLEPc has several iterative eigenanalysis routines which are well-suited to this purpose.

[Theodore Omtzigt]

Hi John:

I was familiar with the SLEPc approach. Vicente gave an overview of SLEPc at the FEniCS workshop in Delft in 2006. What I didn't know was that libMesh is leveraging it as well. I only focused on the FEA code examples in libMesh so I missed the eigen problem stuff.

Can you elaborate a little more on how the eigen problem code structure is formalized in libMesh?

Also your comment on just finding the extreme eigen values/vectors is well received. Do you know which algorithms SLEPc uses here?