<div style="line-height:1.7;color:#000000;font-size:14px;font-family:arial"><DIV> Thanks very much! I understand.</DIV>
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<DIV> I made a test. If the tolerance is large, PETSc says "converged" but the result is "incorrect" for my use</DIV>
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<DIV>due to the tolerance. While the tolerance is tight, when the rtol reaches a certain value, the result is</DIV>
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<DIV>not changing and it is not equal to the true value. And PETSc says "diverged". As Jed said, I need to either</DIV>
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<DIV>increase the number of iterations or use a better preconditioner. And I think the latter is a better way in</DIV>
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<DIV>my work.</DIV>
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<DIV> Thanks.<BR><BR></DIV>
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<DIV><BR></DIV>>At 2012-07-11 01:45:28,"Mark F. Adams" <mark.adams@columbia.edu> wrote:<BR>
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<DIV>>On Jul 10, 2012, at 10:51 AM, w_ang_temp wrote:</DIV><BR class="Apple-interchange-newline">
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<DIV>> In my opinion, convergence in PETSc is decided by rtol, atol and dtol. The divergent hints just show >that</DIV>
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<DIV>>in the solving process it does not satisfy the rule. The "right" result may be different from the true result >at</DIV>
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<DIV>>the several back decimal places(I mean that they may be the same with four decimal places but may be >not</DIV>
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<DIV>>the same with more decimal places). </DIV></DIV></BLOCKQUOTE>
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<DIV>>No, If you have an rtol=1.e-30 and atol=1.e-300 then your solution will probably be correct to all decimal places even >though PETSc will say you "diverged". You can't be too sure about how many digits of accuracy you have with >simple linear algebra arguments unless your system is extremely well conditioned.</DIV>
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<DIV>>As Jed said if you are doing 10000 iterations are happy with the solution then your tolerances are probably too >tight. Look at the residual history and see if you are stagnating.</DIV><BR>
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<DIV>> Is it right?<BR><BR></DIV>
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<DIV><BR></DIV>>At 2012-07-08 00:28:54,"Mark F. Adams" <<A href="mailto:mark.adams@columbia.edu">mark.adams@columbia.edu</A>> wrote:<BR>
<BLOCKQUOTE style="BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex; PADDING-LEFT: 1ex" id="isReplyContent">>It sounds like your -ksp_rtol is too small. Experiment with looser tolerances until your solution is >not "correct" to see >how much accuracy you want.
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<DIV>>On Jul 7, 2012, at 12:15 PM, w_ang_temp wrote:</DIV><BR class="Apple-interchange-newline">
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<DIV>> Maybe it is a problem of mathematical concept. I compare the result with the true >result which is </DIV>
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<DIV>>computed and validated by other tools. I think it is right if I get the same result.</DIV>
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<DIV><BR></DIV>>>ÔÚ 2012-07-08 00:03:21£¬"Matthew Knepley" <<A href="mailto:knepley@gmail.com">knepley@gmail.com</A>> дµÀ£º<BR>
<BLOCKQUOTE style="BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex; PADDING-LEFT: 1ex" id="isReplyContent">>>On Sat, Jul 7, 2012 at 10:00 AM, w_ang_temp <SPAN dir="ltr"><<A href="mailto:w_ang_temp@163.com" target="_blank">w_ang_temp@163.com</A>></SPAN> wrote:<BR>
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<DIV>>>Hello,</DIV>
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<DIV>>> I am a little puzzled that I get the right result while the converged reason says that 'Linear solve >>did not</DIV>
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<DIV>>>converge due to DIVERGED_ITS iterations 10000'. This infomation means that the >>iterations >reach >the maximum</DIV>
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<DIV>>>iterations. But the result is right now. So why says 'did not converge'? Can I think >>that the result is >>right and </DIV>
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<DIV>>>can be used?<BR></DIV></DIV></BLOCKQUOTE>
<DIV>>>Obviously, your definition of "right" is not the same as the convergence tolerances >>you are using.</DIV>
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<DIV>>> Matt</DIV>
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<DIV>>> Thanks.</DIV>
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<DIV>>> Jim</DIV></DIV><BR><BR><SPAN title="neteasefooter"><SPAN></SPAN></SPAN></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></BLOCKQUOTE></DIV><BR><BR><SPAN title="neteasefooter"><SPAN id="netease_mail_footer"></SPAN></SPAN></BLOCKQUOTE></DIV><BR></DIV></BLOCKQUOTE></DIV><BR><BR><SPAN title="neteasefooter"><SPAN id="netease_mail_footer"></SPAN></SPAN></BLOCKQUOTE></DIV><BR></BLOCKQUOTE></div><br><br><span title="neteasefooter"><span id="netease_mail_footer"></span></span>