Hi Ankang, Thanks for sending the bug reports! I've only looked at bug (1) so far. The interpolation error is quite interesting and I agree not necessarily accurate in the vicinity of the interpolation points in its present form. In your example, the interpolation is quite close indeed and perhaps closer than we would usually do this, which may explain why this has not come up before. I was therefore wondering what lead you to find this inaccuracy, just so I can better understand the context a bit? However the 'traditional implementation' of the Lagrange interpolant as you've written it is also numerically unstable (I believe) for larger numbers of interpolation points. We might consider using a barycentric form, as explained in the following two articles: https://people.maths.ox.ac.uk/trefethen/mythspaper.pdf http://www.maths.manchester.ac.uk/~higham/narep/narep440.pdf Don't know if someone with more knowledge of this might be able to weigh in on this aspect! On the m_pressureCalls issue -- I agree one can get a first-order approximation from the first timestep onwards. Not sure why the original implementation doesn't have this. Dave
On 14 Apr 2017, at 13:06, Ankang Gao <gaoak@pku.edu.cn> wrote:
Hellow,
I have found two bugs in the codes, and I listed them in the attachment.
I have a question about why the backward differentiation formula starts after m_pressureCalls>2, in function void Nektar::Extrapolate::AccelerationBDF(Array< OneD, Array< OneD, NekDouble > > & array). Since when m_pressureCalls=2, we can already get a first order accuracy result.
thanks
Ankang <reportbug_question.pdf>_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/nektar-users