Re: [Geopdes-users] Second derivatives of nurbs basis functions

[Rafael V. <va...@im...>]

Dear Lee,
there is a new PhD student in Pavia that has just started the 
implementation of second order derivatives in GeoPDEs, with an example 
of a fourth order problem. As soon as the code is ready and tested we 
will release it, but It will take some time.

If you want to do it yourself, it should not be difficult. In 2D, the 
second derivatives are already computed for a spline space with a NURBS 
geometry. For NURBS, you should add the computation of the second 
derivatives in the parametric domain in the functions bsp_2_nrb_*. The 
derivatives in the physical domain are computed as in the case of splines.

And please, feel free to give me any comment or suggestion about version 
2. Feedback from the users is very welcome.

Regards,
Rafa

Il 25/11/2012 15:52, 李新康 ha scritto:
> Dear Rafael Vazquez,
>         These days I am thinking on how to compute the second derivative of nurbs basis functions. I notice in GeoPDEs 1.0(I still use GeoPDEs version 1.0 because I think it is less difficult to understand than version 2), there are functions  'sp_bspline_2d_param' and 'sp_bspline_2d_phys' that can compute the second derivative of nurbs basis functions in parametric domain and physics domain respectively by making the option 'hessian' true, however, there's no function compute the second derivative of  nurbs functions.
>         There are some mechanics problems need the second derivative of nurbs basis functions, such as Kichhoff plate problem. I find it is too difficult for me to add a function myself, so I ask for your help. Could you add a function in GeoPDEs that can get the hessian matrix of Gauss quadrature points in physical domain in structure 'sp', something like sp_nurbs_2d_phys(sp,msh,'gradient',ture,'hessian,true') and then we can get 'sp.shape_function_hessians' in structure 'sp'?
>         I am very appreciate for your help.
>         Thank you very much!
>
>
> Yous sincerely,
> Lee
>