Simon, If you are willing to do some work, Bernstein basis functions are implemented in deal.II (which are B-spline basis with C0 continuity).
You could exploit BezierExtractor https://onlinelibrary.wiley.com/doi/full/10.1002/nme.2968 and use the facilities of deal.II to work with cubic B-Splines. This is implemented in deal.II, and available with poor documentation, here: https://github.com/mathLab/IGA-dealii You can learn about the data structures by looking at https://iris.sissa.it/retrieve/dd8a4bf7-09b3-20a0-e053-d805fe0a8cb0/1963_35160_Tezzele_tesi.pdf Let me know if you need assistance in using the relative classes. There are two examples that solve a poisson problem and an obstacle problem. We’ll try to make this a gallery example to make it more accessible. L. > On 19 Feb 2023, at 20:45, Wolfgang Bangerth <bange...@colostate.edu> wrote: > > On 2/15/23 06:50, Simon wrote: >> my objective is to do an 1d-approximation >> F(x) = N_i(x) P_i >> where N_i are cubic B-spline basis functions and P_i known nodal values >> (control points). >> To assemble my linear system, I have to compute the first and second >> derivatives of F at the quadrature points of the triangulation. >> Since the number of control points P_i is quite moderate (less than 20), I >> think it is reasonable to evaluate all basis functions N_i in lieu of >> implementing an entire finite element class. >> I scanned the dealii manual but could only find a CSpline class >> <https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.dealii.org%2Fcurrent%2Fdoxygen%2Fdeal.II%2FclassFunctions_1_1CSpline.html&data=05%7C01%7CWolfgang.Bangerth%40colostate.edu%7C9ac052e12d814289384108db0f5b957c%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C638120658249146546%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=NqcY%2FpN5QJnuhVYWG3BiLLKxYUZIZNyYDCKKEDq3iYI%3D&reserved=0>. >> Just to make sure: >> B-Spline (basis) functions are not implemented in dealii yet, right? > > Simon -- that is correct. I suspect (but don't know) that you also want to > use spline basis functions that span across more than one cell; that is an > uncommon operation for finite element libraries and there is not much support > implemented for these kinds of things -- in particular, there are none of the > spline basis functions one might use for this. > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bange...@colostate.edu > www: http://www.math.colostate.edu/~bangerth/ > > > -- > The deal.II project is located at http://www.dealii.org/ > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > --- You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to dealii+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/94d2fa54-291e-97dd-189d-01826aa687a2%40colostate.edu. -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/647A374C-4D71-4204-9238-B27226D399C2%40gmail.com.
