dolfin team mailing list archive

["Johan Hoffman" <jhoffman@xxxxxxxxxx>]

> On Wed, May 09, 2007 at 04:16:01PM +0200, Johan Hoffman wrote:
>> > What is the status of mesh refinement?
>> >
>> > What does work and what does not work?
>>
>> We (me and Johan Jansson) have implemented a bisection mesh refinement
>> algorithm that is dimension independent, and also a mesh coarsening
>> algorithm that is dimension independent. Johan has also implemented a
>> general projection operator that projects a function from one
>> mesh+function space to another mesh+function space. These algorithms
>> appear to be in good shape. What is needed is some more testing,
>> cleaning
>> up, and a demo, which is under way.
>>
>> I have also implemented a class for a hierarchy of meshes, and started
>> to
>> re-implement the old Bey-algorithm for this structure.
>
> Good, but why is the Bey algorithm needed? Does it do things the new
> bisection doesn't?

Both algorithms have their pros and cons. The problem with the bisection
refinement is that it may produce meshes with many edges connected to some
vertices, this is avoided in the Bey algorithm since here we only cut
edges. And the bisection-coarsening is worse in this respect. The remedy
is to couple this with edge-flips and face-swaps (changing connectivity).

The great thing about bisection is that it is dimension independent, it
does not introduce hanging nodes, and it is simple.

>> On the mesh refinement/coarsening todo-list we next have: edge-flip and
>> face-swaps, and finishing the Bey-algorithm. We are also working on some
>> mesh smoothing algorithms together with Michael Stöckli.
>>
>> /Johan
>
> Good, I'm just trying to get a feeling for what we need to do before
> the next release and one of them is to get the mesh demo working.

Yes, I think we should be able to complement that demo with mesh
refinement/coarsening/projection.

/Johan


> /Anders
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