[Dune] Dune::HierarchicalOrthogonalShapeFunctionSet< C, T, d > Class Template Reference

[Tatiana Voitovich]

Dear colleages,

I am sorry for the inconvienience, in the previous letter there had been
no the text of the letter of Christian Engwer included. I send you the
same letter with the text of the answer.

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Thank you very much for your answer!

>> could you please let me know, on what it depends, which version --- svn or
>> release to use
>> for implementing a certain numerical scheme in DUNE+DUNE-fem.
>
> Please look through the recent changes, whether there are any
> features, whihc require you to use the development branch.

As far as I have understood, I will need to use the new package dune-disc.
To be precise, I will have to write a class, perhaps useful for many users
of dune, alternative to

Dune::MonomialShapeFunctionSet< C, T, d > Class Template Reference

which could have the name

Dune::HierarchicalOrthogonalShapeFunctionSet< C, T, d > Class Template
Reference,

or

Dune::GeneralizedTensorProductShapeFunctionSet< C, T, d > Class Template
Reference

which will be a dune implementation of an hierarchical orthogonal basis
functions set introduced independently by  Proriol, Karlin and McGregor,
Koornwinder and Dubiner and traditionally employed by $hp-$ spectral
finite element methods, you could have a look in T. Warburton, An explicit
construction of interpolation nodes on the simplex, J. Eng. Math. (2006),
247-262.
The matter, in addition to the orthogonality property, why we would
like to use this set, is that those basis functions contain in their
expressions Jacobi polynomials, therefore the diagonal mass matrix is good
conditioned, while the (cartesian coordinates) monomials function set is
nearly linear dependent for p results in a mass matrix that is nearly
singular starting from the degree of interpolation
polynomials $p \gtrsim 7$ (see, f.e. M. Dubiner, Spectral methods on
triangles and other domains, 1991).

As far as I know, deal II, a structured-grid-branch, employes this basis
set extensively.

For this shape function set I have the local elemental operations (such as
quadrature approximation of the mass matrix) implemented and tested in C.

With best regards,
Tatiana





>> could you please let me know, on what it depends, which version --- svn
>> or
>> release to use
>> for implementing a certain numerical scheme in DUNE+DUNE-fem.
>
> Please look through the recent changes, whether there are any
> features, whihc require you to use the development branch.
>
>> If there are
>> a lot of support added  in svn-version for making the development
>> process
>> easier?
>
> No. It is always more tricky to work with the development branch, as
> the code might be changing a lot. We make no guarantee to not break
> you code. So you will alwways have to take care keeping your code
> running.
>
> For newbies I'd always recommend the stable version.
>
>> Would it cause problems having both versions on one computer?
>
> As long as you know what you are doing you can have as many different
> versions of dune on your computer as you like. But you must configure
> your environment accordingly.
>
> Judging you unix shell skills (sorry if I miss estimate these) I'd
> guess, that you should not try to use these different versions of
> Dune. There is no documentation on this and we can not give you any
> support. These issues are not Dune related but are a question of
> whether you are a "hard core -- I know know all the dirty tricks" user
> of your favorite operating system or a "I just want it to work" user.
>
> Hope I coud answer you questions, again I encourage you to use the
> stable release and to use just these features you are sure you need.
>
> Cheers Christian
>