On Fri, Dec 23, 2011 at 1:27 PM, Jed Brown <span dir="ltr"><<a href="mailto:jedbrown@mcs.anl.gov">jedbrown@mcs.anl.gov</a>></span> wrote:<br><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div class="gmail_quote">On Fri, Dec 23, 2011 at 12:52, Dominik Szczerba <span dir="ltr"><<a href="mailto:dominik@itis.ethz.ch" target="_blank">dominik@itis.ethz.ch</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>I am scaling my systems when dealing with small (microscopic) scales<br>
in SI dimensions. </div></blockquote><div><br></div><div>The best choice is to choose suitable units so that the system is intrinsically well-scaled.</div></div></blockquote><div><br></div><div>I think the best approach is always to non-dimensionalize after taking input in your favorite</div>
<div>units. We do this in PyLith. On output, just put the dimension back in. It also lets you see</div><div>the scaling factors explicitly, which is useful for reasoning physically about the problem.</div><div><br></div><div>
Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class="gmail_quote"><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>This is because otherwise I have very small (near<br>
epsilon) entries in the matrix and the solution fails or takes<br>
significantly longer to converge. I used to do it by hand so far, if<br>
there is a way to do it in Petsc - especially automatically detecting<br>
the optimal scale - I am all ears.</div></blockquote></div><br><div>You are best off doing it by hand, it is better to avoid -ksp_diagonal_scale when it's reasonable to do so. If you have trouble determining a reasonable scale at assembly time, it might make sense to use.</div>
</blockquote></div><br><br clear="all"><div><br></div>-- <br>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<br>