On Thu, Jan 31, 2019 at 6:22 PM Justin Chang <jychan...@gmail.com> wrote:
> 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. > Maybe I am reading this wrong, but the Y-bus matrix looks like an M-matrix to me (if all the y's are positive). This means that it should be really easy to solve, and I think GAMG should do it. You can start out just doing relaxation, like SOR, on small examples. Thanks, Matt > On Thu, Jan 31, 2019 at 1:47 PM Matthew Knepley <knep...@gmail.com> wrote: > >> On Thu, Jan 31, 2019 at 3:20 PM Justin Chang via petsc-users < >> petsc-users@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/> >> > -- 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/>