<div dir="ltr"><div dir="ltr">On Thu, Jan 31, 2019 at 6:22 PM Justin Chang <<a href="mailto:jychang48@gmail.com">jychang48@gmail.com</a>> wrote:<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr">Here's IMHO the simplest explanation of the equations I'm trying to solve:<div><br></div><div><a href="http://home.eng.iastate.edu/~jdm/ee458_2011/PowerFlowEquations.pdf" target="_blank">http://home.eng.iastate.edu/~jdm/ee458_2011/PowerFlowEquations.pdf</a><br></div><div><br></div><div>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.</div></div></div></blockquote><div><br></div><div>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</div><div>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</div><div>small examples.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Jan 31, 2019 at 1:47 PM Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr">On Thu, Jan 31, 2019 at 3:20 PM Justin Chang via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>> wrote:<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr">Hi all,<div><br></div><div>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. </div><div><br></div><div>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.</div><div><br></div><div>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.</div></div></blockquote><div><br></div><div>1) We really need to see the (simplified) equations</div><div><br></div><div>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</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>Justin</div></div>
</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail-m_4182101500591969802gmail-m_-7596872824010350421gmail-m_8922927719976317655gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>
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</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>