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

[Justin Chang]

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.

On Thu, Jan 31, 2019 at 1:47 PM Matthew Knepley <knepley at gmail.com> wrote:

> 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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