Hi Konstantin, One option would be to employ a combination of a transfer function and level set functions. With this approach you effectively provide a regularised expression for the material parameters. You can see how this is done equation 18 in this paper <http://dx.doi.org/10.1007/s00466-015-1224-4> and equation 32 in this paper <http://doi.org/10.1007/s00466-016-1329-4>. If you can't access either of the articles then let me know and I can provide some further details.
I hope that this helps! Regards, J-P On Tuesday, May 2, 2017 at 2:11:57 PM UTC+2, Konstantin Ladutenko wrote: > > Hi all, > > What is the correct way to set smooth coefficients in space for high > p-order of elements simulation in deal.ii? > > E.g. in Step-6 nonconstant coefficient is a step function alpha=20 for > R<0.5 and alpha=1 otherwise (0<R<1). How to set it to be a smooth > function, e.g. some polynomial function of order 'n' like > alpha=20*(1-R^n)+1? So it should be enough to use few high-order elements > for the whole model to converge to the smooth solution. > > I`ve checked a number of tutorials (e.g. > http://www.dealii.org/developer/doxygen/deal.II/step_4.html#Righthandsideandboundaryvalues > > , equation data section in step-27, and few others - all of them use a > point-wise approximation of an analytic function (so it is tuned for > h-refinements), which is practically the same as a step function for a > given mesh. > > This is actually very important when solving any open-boundary problem > using perfectly-matching layer (PML), as soon as the latter needs to have a > parameter grading (conductivity). Any ideas\examples how it can be done > using deal.ii? > > As an external reference, there is a PhD thesis > http://arizona.openrepository.com/arizona/handle/10150/195940 with a > description of a single cell PML. In a short, it is preferable to use one > high-p element to set PML from the point of view of performance (wave > reflection) to DoF ratio. > > Best regards, > Konstantin Ladutenko > > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. For more options, visit https://groups.google.com/d/optout.
