<div class="gmail_quote">On Wed, Feb 22, 2012 at 18:05, Patrick Alken <span dir="ltr"><<a href="mailto:patrick.alken@colorado.edu">patrick.alken@colorado.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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>
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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><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></blockquote><div><br></div>
<div>What sort of PDE are you solving?</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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I was wondering if this phenomenon is common in PDEs? and if there is any way to correct for it?<br>
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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>
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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>
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Any advice from those who have experience with this phenomenon would be greatly appreciated!<br>
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Thanks,<br><font color="#888888">
Patrick<br>
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