[Dune] Handling checkinside for curvilinear elements

[Andreas Dedner]

Hi.
I think all your problems boil down to the last one: implementing the
method local.
If you have local then a point is a global point x is within an element
if local(x) is within the
reference element. That is what we use for the hoerarchicSearch class (a
utility class in
dune grid which should then be directly useable for your second point).
I don't think I understand your first problem since you are still using
the same reference element, right?
So a condition for a point being inside the reference element has
nothing to do with your global mapping,
be it straight faced or not.
Best
Andreas

On 28/07/14 16:55, Aleksejs Fomins wrote:
> Dear Dune,
>
> I am currently implementing curvilinear tetrahedral grid for dune.
>
> The following functionality will be required:
>
> 1) dune/geometry/genericreferenceelements.hh has function isinside()
> which checks whether the point is inside of the tetrahedron. This
> functionality will not be valid for curvilinear tetrahedrons.
>
> Where should I implement the new functionality? Should I directly edit
> the genericreferenceelements.hh or should I define a new method inside
> my new version of multilineargeometry.hh, or sth else?
>
> Where is this functionality used?
>
> Also, if you have suggestions on how to mathematically check this,
> please advise me. I have a conjecture that the point is inside if it is
> on the correct side of each face, and it is on the correct side of the
> face if det(d, v1, v2) has the right sign, where d is the distance
> vector between this point and the closest point on the surface, and v1
> and v2 are the surface tangential unit vectors given by the parametric
> coordinates.
>
> 2) We personally would really need the functionality of finding the
> tetrahedron to which a given global coordinate belongs. Extending this
> to curvilinear is trivial - first find the element to which it would
> have belonged to if the tetrahedrons were straight-sided, then check
> whether it is actually inside this tetrahedron or one of its neighbors
> using the isinside() method.
>
> Is this (straight-sided) functionality already implemented in dune
> somewhere? Is it efficient? I mean, whether it loops over all elements
> and checks isinside(), or whether it uses something more sophisticated
> like octrees.
>
> 3) Another mathematics-related question. To map from local to global
> coordinates within an element I simply evaluate the linear combination
> of lagrange polynomials.
>
> How do I map from global to local?
>
> The best thing that comes to my mind is to write an iterative
> optimization algorithm minimizing the distance between given local
> coordinate and the expected one. It will have to be random like MCMC
> because the problem will have local minima. Please comment if you have
> good ideas :)
>
> Thank you,
> Aleksejs
>
>
>
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