<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div>Hi,</div><div><br></div><div>Ata and I are working together on this. The problem he describes is 1/2 of the iteration of our variational fracture code. </div><div>In our application, E is position dependant, and typically becomes very large along very thin bands with width of the order of epsilon in the domain. Essentially, we expect that V will remain exactly equal to 1 almost everywhere, and will transition to 0 on these bands. Of course, we are interested in the limit as epsilon goes to 0. </div><div><br></div><div>If the problem indeed is that it takes many steps to add the degrees of freedom. Is there any way to initialize manually the list of active constraints? To give you an idea, here is a link to a picture of the type of solution we expect. blue=1</div><div><a href="https://www.math.lsu.edu/~bourdin/377451-0000.png">https://www.math.lsu.edu/~bourdin/377451-0000.png</a></div><div><br></div><div>Blaise</div><div><br></div><div><br></div><div><br></div><div><blockquote type="cite">It seems to me that the problem is that ultimately ALL of the degrees of freedom are in the active set,<div>but they get added to it a few at a time -- and there may even be some "chatter" there -- necessitating many SNESVI steps. </div>
<div>Could it be that the regularization makes things worse? When \epsilon \ll 1, the unconstrained solution is highly oscillatory, possibly further exacerbating the problem. It's possible that it would be better if V just diverged uniformly. Then nearly all of the degrees of freedom would bump up against the upper obstacle all at once. </div>
<div><br></div><div>Dmitry.<br><br><div class="gmail_quote">On Mon, Jan 16, 2012 at 8:05 PM, Barry Smith <span dir="ltr"><<a href="mailto:bsmith@mcs.anl.gov">bsmith@mcs.anl.gov</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
What do you get with -snes_vi_monitor it could be it is taking a while to get the right active set.<br>
<span class="HOEnZb"><font color="#888888"><br>
Barry<br>
</font></span><div class="HOEnZb"><div class="h5"><br>
On Jan 16, 2012, at 6:20 PM, Ataollah Mesgarnejad wrote:<br>
<br>
> 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<br>
<br>
</div></div></blockquote></div><br></div>
</blockquote></div><br><div apple-content-edited="true">
<div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; font-size: 12px; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; -webkit-text-decorations-in-effect: none; text-indent: 0px; -webkit-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">-- </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Department of Mathematics and Center for Computation & Technology</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Louisiana State University, Baton Rouge, LA 70803, USA</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Tel. +1 (225) 578 1612, Fax +1 (225) 578 4276 <a href="http://www.math.lsu.edu/~bourdin">http://www.math.lsu.edu/~bourdin</a></div><div><br class="khtml-block-placeholder"></div><div><br class="khtml-block-placeholder"></div><br class="Apple-interchange-newline"></div></span></div></span><br class="Apple-interchange-newline"></div><br class="Apple-interchange-newline"><br class="Apple-interchange-newline">
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