Re: [Libmesh-devel] FE::inverse_map() not converging...

[Roy S. <roy...@ic...>]

On Thu, 22 Jun 2006, Derek Gaston wrote:

> elem::contains_point() is using the same flawed logic to decide
> whether or not the point is contained in the element (meaning the
> newton iterations).  What's happening is that the newton iterations
> are failing to converge so severely that the final guess as where the
> point is... actually lies within the element!  Thus giving a false
> positive.

This is what I was afraid of - the fix is as I suggested the other
day: if the Newton iteration doesn't converge, return a point like
(1.e6,1.e6,1.e6) so we don't get a false positive from
contains_point().

> So here's the deal... inverse_map is _NOT_ a good idea to use for
> finding out if the point lies within the element!

I think I disagree.  These Newton failures should only happen if the
element is badly twisted or if the point is outside the element,
right?  So in that case, if we just return a junk point when Newton
fails, we should still get correct results.

> My question is this: contains_point() is a virtual function right?
> Can we not just override it in the concrete classes so that we don't
> have to do this newton thing at all?  I mean a quad4 should be able to
> figure out pretty quickly whether or not a point lies in it....
> without all the newton iteration stuff.  Sure we can leave the newton
> stuff to fall back on in case we don't want to implement
> contains_point in a concrete_class... but for elements for which it
> would be easy (maybe even trivial?) to do it for manually... why not?

> PS: Yes, this is me "volunteering" to go write contains_point()
> functions for all our dang elements ;-)

Works for me!  I'm not sure how much of an improvement you can make in
general, but at the very least it might be a little optimization for
TRI3/QUAD4.

For the more complicated geometric elements you might try testing
has_affine_map() first - if the element transformation is affine (and
I don't know about your weird smoothed meshes but in my meshes most of
the elements are affine) then you can implement contains_point with
n_sides inequality tests.
---
Roy