[petsc-users] Preconditioning systems of equations with complex numbers

[Jed Brown]

Justin Chang via petsc-users <petsc-users at mcs.anl.gov> writes:

> Here's IMHO the simplest explanation of the equations I'm trying to solve:
>
> http://home.eng.iastate.edu/~jdm/ee458_2011/PowerFlowEquations.pdf
>
> Right now we're just trying to solve eq(5) (in section 1), inverting the
> linear Y-bus matrix. Eventually we have to be able to solve equations like
> those in the next section.

It's always useful to pick a smallish problem and compute the spectrum
of the operator and plot the eigenvectors associated with interesting
eigenvalues (especially those near zero and those with largest
magnitude).  Eq 5 looks like a graph Laplacian.