<div class="gmail_quote">On Thu, Dec 22, 2011 at 20:50, Mohamad M. Nasr-Azadani <span dir="ltr"><<a href="mailto:mmnasr@gmail.com">mmnasr@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><span style="font-family:'Times New Roman';text-align:-webkit-left;background-color:rgb(255,255,255);font-size:medium">1) As mentioned on the web when we use </span></div>
<div><b style="font-family:'Times New Roman';text-align:-webkit-left;background-color:rgb(255,255,255);font-size:medium">-ksp_diagonal_scale_fix: </b><span style="font-family:'Times New Roman';background-color:rgb(255,255,255);font-size:medium">scale the matrix back AFTER the solve</span></div>
<div><span style="font-family:'Times New Roman';background-color:rgb(255,255,255);font-size:medium"><br></span></div><div><span style="font-family:'Times New Roman';background-color:rgb(255,255,255);font-size:medium">with -ksp_diagonal_scale d</span><span style="font-family:'Times New Roman';background-color:rgb(255,255,255);font-size:medium">oes it also scale back the RHS vector associated with the KSP solver? </span></div>
</blockquote><div><br></div><div>yes</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><span style="font-family:'Times New Roman';background-color:rgb(255,255,255);font-size:medium"><br></span></div><div><span style="font-family:'Times New Roman';background-color:rgb(255,255,255);font-size:medium">2) Also, as mentioned on the web for -ksp_diagonal_scale</span></div>
<div><span style="font-family:'Times New Roman';background-color:rgb(255,255,255);font-size:medium">"Tells </span><a href="http://www.mcs.anl.gov/petsc/petsc-3.1/docs/manualpages/KSP/KSP.html#KSP" style="font-family:'Times New Roman';background-color:rgb(255,255,255);font-size:medium" target="_blank">KSP</a><span style="font-family:'Times New Roman';background-color:rgb(255,255,255);font-size:medium"> to symmetrically diagonally scale the system before solving. "</span></div>
<div><span style="font-family:'Times New Roman';background-color:rgb(255,255,255);font-size:medium"><br></span></div><div><font face="'Times New Roman'" size="3">When I used this option to solve for the Pressure (Poisson equation with Neumann B.C., descritized via structured fisytenite-difference method), the number of iterations for convergence was trippled, e.g. without this option, it converges in 18 iteration, but with this option it goes up to 50-60 iterations. </font></div>
<div><font face="'Times New Roman'" size="3">(GMRES + BoomerAMG as the preconditioner). </font></div><div><font face="'Times New Roman'" size="3">Is this something you would expect? </font></div></blockquote>
<div><br></div><div>It's perhaps slightly surprising that it's that much worse, but there is nothing saying that the diagonal scaled matrix will be better. Most preconditioners correct the diagonal scaling.</div><div>
</div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><font face="'Times New Roman'" size="3"><br></font></div><div><font face="'Times New Roman'" size="3">3) How could the linear system resulting from the Poisson equation for pressure (incompressible flow) can be more diagonally scaled? To elaborate more, for the uniform grid case and let's say a second order central scheme finite difference discretization, the sum of the off-diagonal coefficients are equal to the diagonal coefficient. </font></div>
</blockquote></div><br><div>You probably don't have a reason to use diagonal scaling.</div>