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On 02/22/2012 05:13 PM, Jed Brown wrote:
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cite="mid:CAM9tzSkqM7=TS8UYnFCdJcB7zdxjUBKgSLv_HCCnSb2+HvMbrQ@mail.gmail.com"
type="cite">
<div class="gmail_quote">On Wed, Feb 22, 2012 at 18:05, Patrick
Alken <span dir="ltr"><<a moz-do-not-send="true"
href="mailto:patrick.alken@colorado.edu">patrick.alken@colorado.edu</a>></span>
wrote:<br>
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Hi all,<br>
<br>
I have been trying to track down a problem for a few days
with solving a linear system arising from a finite differenced
PDE in spherical coordinates. I found that PETSc managed to
converge to a nice solution for my matrix at small grid sizes
and everything looks pretty good.<br>
<br>
But when I try larger more realistic grid sizes, PETSc fails
to converge. After trying with another direct solver library,
I found that the direct solver found a solution which exactly
solves the matrix equation,</blockquote>
<div><br>
</div>
<div>This never happens, so what do you mean? You compute the
residual and it's similar to what you expect the rounding
error to be?</div>
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<br>
Yes I mean the direct solver residual is around 10e-15. The PETSc
residual is 4e00<br>
<br>
<blockquote
cite="mid:CAM9tzSkqM7=TS8UYnFCdJcB7zdxjUBKgSLv_HCCnSb2+HvMbrQ@mail.gmail.com"
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<div class="gmail_quote">
<div> </div>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex"> but when
plotting the solution, I see that it oscillates rapidly
between the grid points and therefore isn't a satisfactory
solution. (At smaller grids the solution is nice and smooth)<br>
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<div>What sort of PDE are you solving?</div>
</div>
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<br>
The PDE is:<br>
<br>
grad(f) . B = g<br>
<br>
where B is a known vector field, g is a known scalar function, and f
is the unknown scalar function to be determined (I am discretizing
this equation for f in spherical coords)<br>
<br>
<blockquote
cite="mid:CAM9tzSkqM7=TS8UYnFCdJcB7zdxjUBKgSLv_HCCnSb2+HvMbrQ@mail.gmail.com"
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<div> </div>
<blockquote class="gmail_quote" style="margin:0 0 0
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<br>
I was wondering if this phenomenon is common in PDEs? and if
there is any way to correct for it?<br>
<br>
I am currently using 2nd order centered differences for
interior grid points, and 1st order forward/backward
differences for edge points. Would it be worthwhile to try
moving to 4th order differences instead? Or would that make
the problem worse?<br>
<br>
I've even tried smoothing the parameters which go into the
matrix entries using moving averages...which doesn't seem to
help too much.<br>
<br>
Any advice from those who have experience with this
phenomenon would be greatly appreciated!<br>
<br>
Thanks,<br>
<font color="#888888">
Patrick<br>
</font></blockquote>
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