<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div><br></div><blockquote type="cite">What is the solution that you end up converging to</blockquote><div><br></div>I get the correct solution.</div><div><br><blockquote type="cite">, and what are the boundary conditions?<div><br></div></blockquote>I have natural BCs everywhere ( dV/dn=0) so I don't force it explicitly.</div><div><br></div><div>Ata</div><div><br><blockquote type="cite"><div>Thanks.</div><div>Dmitry.<br><br><div class="gmail_quote">On Mon, Jan 16, 2012 at 6:20 PM, Ataollah Mesgarnejad <span dir="ltr"><<a href="mailto:amesga1@tigers.lsu.edu">amesga1@tigers.lsu.edu</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Dear all,<br>
<br>
I'm trying to use SNESVI to solve a quadratic problem with box constraints. My problem in FE context reads:<br>
<br>
(\int_{Omega} E phi_i phi_j + \alpha \epsilon dphi_i dphi_j dx) V_i - (\int_{Omega} \alpha \frac{phi_j}{\epsilon} dx) = 0 , 0<= V <= 1<br>
<br>
or:<br>
<br>
[A]{V}-{b}={0}<br>
<br>
here phi is the basis function, E and \alpha are positive constants, and \epsilon is a positive regularization parameter in order of mesh resolution. In this problem we expect V =1 a.e. and go to zero very fast at some places.<br>
I'm running this on a rather small problem (<500000 DOFS) on small number of processors (<72). I expected SNESVI to converge in couple of iterations (<10) since my A matrix doesn't change, however I'm experiencing a slow convergence (~50-70 iterations). I checked KSP solver for SNES and it converges with a few iterations.<br>
<br>
I would appreciate any suggestions or observations to increase the convergence speed?<br>
<br>
Best,<br>
Ata</blockquote></div><br></div>
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