[Users] Instabilities with Summation by Parts 4th order operator

Miguel Zilhão miguel.zilhao.nogueira at tecnico.ulisboa.pt
Thu May 7 14:20:33 CDT 2020

hi Peter,

thanks for having a look. i've just replied to the ticket.
indeed, setting SummationByParts::operator_type = "Minimal Bandwidth" does seem to lead to stable 


On 07/05/20 14:59, Peter Diener wrote:
> Hi Miguel,
> I have commented on the ticket you created about this. Please take a look at that comment and let me 
> know what you think.
> Cheers,
>    Peter
> On Thursday 2020-04-09 13:08, Miguel Zilhão wrote:
>> Date: Thu, 9 Apr 2020 13:08:47
>> From: Miguel Zilhão <miguel.zilhao.nogueira at tecnico.ulisboa.pt>
>> To: Einstein Toolkit Users <users at einsteintoolkit.org>
>> Subject: [Users] Instabilities with Summation by Parts 4th order operator
>> hi all,
>> i've been working on implementing the Summation by Parts (SBP) operators on some evolution codes i 
>> have and i was seeing some instabilities when using the 4th order accurate 2nd derivative operator.
>> in order to try to understand the problem better, i've coded a very simple thorn that evolves the 
>> wave equation in first-order in time, second-order in space form. i can evolve the system just 
>> fine without any problems with the SBP operators of order 2, 6 and 8. with order 4, however, there 
>> are instabilities propagating from the boundary that crash the code very early on. has anyone seen 
>> something like this before? could there be a bug in the 4th order 2nd derivative SBP operators, or 
>> am i doing something wrong? i find it very strange that it only crashes with the 4th order 
>> accurate 2nd derivative SBP stencils (the code also seems to run fine with the parameter 
>> SummationByParts::sbp_2nd_deriv = no)...
>> i've uploaded this thorn (called IST_WaveToy) here: https://github.com/mzilhao/IST_WaveToy
>> i tried to keep everything as simple as possible. i'm attaching the thornlist used to checkout and 
>> compile the code, and in the repository i've also added the parameter files i tried with the 
>> different SBP orders (under ./par).
>> any help or comments would be appreciated.
>> thanks,
>> Miguel

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