On Fri, Oct 19, 2012 at 9:02 AM, Anton Popov <span dir="ltr"><<a href="mailto:popov@uni-mainz.de" target="_blank">popov@uni-mainz.de</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">
Of, course you have a more sophisticated case, but if you just put the orders of magnitude of your matrix blocks<br>
into a toy two-by-two matrix, i.e. (in matlab notation)<br>
A = [1e9, 1; 1, 1e-9]<br>
then it's immediately visible that A is singular (det(A) is zero)<br>
Symmetric scaling, that Matt suggested, just makes it more obvious, after scaling the matrix A will be:<br>
A = [1, 1; 1, 1] - clearly the rows are linearly dependent.<br>
Scaling may help you, but of course, this is not an always working solution<br></blockquote><div><br></div><div>These are just the scales, not the values. Thus the matrix need not be singular.</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">
Anton<br>
<br>
On 10/18/12 8:38 PM, Nachiket Gokhale wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
On Thu, Oct 18, 2012 at 2:28 PM, Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
On Thu, Oct 18, 2012 at 11:07 AM, Nachiket Gokhale <<a href="mailto:gokhalen@gmail.com" target="_blank">gokhalen@gmail.com</a>><br>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Hi,<br>
<br>
I am solving a Piezoelectric problem using Petsc. The structure is<br>
<br>
[ K_uu K_uv ]<br>
[K_uv ^T -K_v,v ]<br>
<br>
More details about the formulation: <a href="http://tinyurl.com/9hlbp4u" target="_blank">http://tinyurl.com/9hlbp4u</a><br>
<br>
K_uu has elements O(1E9) because the stiffnesses are in GPa,<br>
K_uv has elements O(1) because piezoelectric coefficients are of that<br>
order<br>
K_v,v has elements O(1E-9) because the dielectric constants are of<br>
that order.<br>
<br>
I am using Petsc, with pc_type LU and MUMPS for the factorization,<br>
-ksp_type gmres. I am not sure if my solution is converging. A typical<br>
solve seems to be doing this:<br>
<br>
28 KSP preconditioned resid norm 5.642364260456e-06 true resid norm<br>
1.228976487745e-03 ||r(i)||/||b|| 3.317409023627e-14<br>
29 KSP preconditioned resid norm 5.540718271043e-06 true resid norm<br>
1.228453548651e-03 ||r(i)||/||b|| 3.315997440178e-14<br>
30 KSP preconditioned resid norm 1.973052106578e-03 true resid norm<br>
1.220399172500e-03 ||r(i)||/||b|| 3.294256047735e-14<br>
31 KSP preconditioned resid norm 1.155762663956e-17 true resid norm<br>
2.447631111938e-04 ||r(i)||/||b|| 6.606955965570e-15<br>
<br>
Is there a right way to solve this set of equations? Is PCFieldSplit<br>
the recommended way?<br>
</blockquote>
<br>
First, you should really non-dimensionalize. You can see what this would<br>
give<br>
you by symmetrically scaling your problem with [ 3e4 3e-4 ], namely<br>
everything<br>
will be O(1).<br>
<br>
Second, you might get something out of using FieldSplit, but its tough to<br>
tell<br>
without knowing more about the operators.<br>
<br>
Matt<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Thanks,<br>
<br>
-Nachiket<br>
</blockquote></blockquote>
Oh, right, thanks. I wasn't even thinking of it that way. I'll scale<br>
the variables and I'll give it a try.<br>
<br>
Cheers,<br>
<br>
-Nachiket<br>
<br>
<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br><span class="HOEnZb"><font color="#888888">
<br>
--<br>
What most experimenters take for granted before they begin their experiments<br>
is infinitely more interesting than any results to which their experiments<br>
lead.<br>
-- Norbert Wiener<br>
</font></span></blockquote></blockquote>
<br>
</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>