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

[Matthew Knepley]

On Thu, Jan 31, 2019 at 3:20 PM Justin Chang via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Hi all,
>
> I'm working with some folks to extract a linear system of equations from
> an external software package that solves power flow equations in complex
> form. Since that external package uses serial direct solvers like KLU from
> suitesparse, I want a proof-of-concept where the same matrix can be solved
> in PETSc using its parallel solvers.
>
> I got mumps to achieve a very minor speedup across two MPI processes on a
> single node (went from solving a 300k dog system in 1.8 seconds to 1.5
> seconds). However I want to use iterative solvers and preconditioners but I
> have never worked with complex numbers so I am not sure what the "best"
> options are given PETSc's capabilities.
>
> So far I tried GMRES/BJACOBI and it craps out (unsurprisingly). I believe
> I also tried BICG with BJACOBI and while it did converge it converged
> slowly. Does anyone have recommendations on how one would go about
> preconditioning PETSc matrices with complex numbers? I was originally
> thinking about converting it to cartesian form: Declaring all voltages =
> sqrt(real^2+imaginary^2) and all angles to be something like a conditional
> arctan(imaginary/real) because all the papers I've seen in literature that
> claim to successfully precondition power flow equations operate in this
> form.
>

1) We really need to see the (simplified) equations

2) All complex equations can be converted to a system of real equations
twice as large, but this is not necessarily the best way to go

 Thanks,

    Matt


> Justin
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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