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.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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