<html>#2368: Instabilities with Summation by Parts thorn 4th order operator
<table style='border-spacing: 1ex 0pt; '>
<tr><td style='text-align:right'> Reporter:</td><td>Miguel Zilhão</td></tr>
<tr><td style='text-align:right'> Status:</td><td>open</td></tr>
<tr><td style='text-align:right'>Milestone:</td><td></td></tr>
<tr><td style='text-align:right'> Version:</td><td></td></tr>
<tr><td style='text-align:right'> Type:</td><td>bug</td></tr>
<tr><td style='text-align:right'> Priority:</td><td>major</td></tr>
<tr><td style='text-align:right'>Component:</td><td>EinsteinToolkit thorn</td></tr>
</table>
<p>Comment (by Peter Diener):</p>
<p>I don’t think I want to change the default operator_type to “Minimal Bandwidth” as this would then also be the default for the 1st derivative operators, where the optimized operators lead to stable (and more accurate) evolutions. What I’m contemplating is just disabling the optimized 4th order second derivative operator and (similarly to the higher order second derivatives) just use the minimal bandwidth, regardless of parameter settings. I believe you might be the first to try to actually use the second derivative operators, so such a change would not affect many people. I will attempt to make a pull request for that.</p>
<p>With SBP operators, there’s always a mismatch between the truncation errors in the interior and the boundary as the order is only half at the boundary compared to the interior. And in fact the optimized operator should have less overall truncation error compared to the minimal bandwidth operator. So I can’t explain why it is less stable. Then again, to have a proper proof of numerical stability in 1 dimension requires that the boundary conditions are implemented using something like a Simultaneous Approximation Term (SAT) methods. It is possible that the optimized operators would be stable if such a boundary method was used.</p>
<p>--<br/>
Ticket URL: <a href='https://bitbucket.org/einsteintoolkit/tickets/issues/2368/instabilities-with-summation-by-parts'>https://bitbucket.org/einsteintoolkit/tickets/issues/2368/instabilities-with-summation-by-parts</a></p>
</html>