Drs. Bruno and Wolfgang, *Actually what Wolfgang is suggesting is very doable. We have wrappers for the ArborX library https://dealii.org/current/doxygen/deal.II/classArborXWrappers_1_1BVH.html <https://dealii.org/current/doxygen/deal.II/classArborXWrappers_1_1BVH.html> which allows you to find the nearest neighbor between two point clouds very efficiently. You should be able to find the closest vertex on the boundary for 100,000 points in a couple of seconds on the CPU and for several millions of points if you are using a GPU. Right now we only have wrappers for the serial version of ArborX but I have actually started to work on the wrappers for distributed tree. When it's done, you will be able to get the nearest neighbor even if they are on different processors.* That would be great! I think it would be very useful for applications like turbulent flows where this information is required.
*The best methods for the eikonal equation are all in the class of "fastmarching method". It has its own wikipedia page:https://en.wikipedia.org/wiki/Fast_marching_method <https://en.wikipedia.org/wiki/Fast_marching_method>* Thank you very much! On Friday, February 11, 2022 at 9:48:16 PM UTC+5:30 Wolfgang Bangerth wrote: > On 2/10/22 22:51, vachan potluri wrote: > > This is a very difficult operation to do even in sequential computations > > unless you have an analytical description of the boundary. That's > because in > > principle you would have to compare the current position with all points > (or > > at least all vertices) on the boundary -- which is very expensive to do > if you > > had to do it for more than just a few points. The situation does not get > > better if you are in parallel, because then you don't even know all of > the > > boundary vertices. > > > > Completely realise and agree. > > I stand corrected by Bruno about this -- I learned something today :-) > > > > The only efficient way to do this sort of operation is to solve an > eikonal > > equation in which the solution function equals the distance to the > boundary. > > You can't solve it exactly, and so whatever distance you get is going to > be a > > finite-dimensional approximation of the exact distance function. > > > > I have got a basic idea of the equation from Wikipedia. Can you kindly > also > > point me to any references which describe its numerical solution > technique? I > > have no background in mathematics, so I have difficulty in understanding > any > > high level content. > > The best methods for the eikonal equation are all in the class of "fast > marching method". It has its own wikipedia page: > https://en.wikipedia.org/wiki/Fast_marching_method > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@colostate.edu > www: http://www.math.colostate.edu/~bangerth/ > > -- 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 dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/37f735a4-6a08-4b09-94a4-0bcfb2e275a5n%40googlegroups.com.
