Hi Robert,
I have been using Sfepy for the past two months now, and the more I use it the more I like it! Thank you for developing this great FEM (& more) software.
I spent some time trying the various functionalities sfepy offers and recently discovered the IGA mode, which I managed to use interactively. After some testing, it turns out isogeometric analysis might be well suited for my applications, where geometry plays a crucial role. So far, my IGA simulations outperform FEM ones, which really sparked my interest for this type of analysis. Having no background in IGA, I read references [1] and [2] to grasp the mathematical concepts at stake, and reference [3] for the Bézier extraction method.
That being said, user's guide mentions that surface terms in IGA are not implemented yet in Sfepy, and I was wondering why?
For instance, I would like to compute integrals over (D-1)-dimensional spaces (where D denotes the problem spatial dimension), but as expected, running the line:
pb.evaluate('ev_surface_integrate.3.Gamma(u)', mode='eval')
results with
ValueError: unknown dof connectivity type! (surface)
This error is raised in sfepy\discrete\iga\fields.py function setup_extra_data.
Of course, I could get around this missing functionality by sampling the scalar field of interest over the desired surface/curve manually (i.e. with field.evaluate_at) and use scipy.integrate. But that would mean giving up on the 'exact' geometry description, which I am not keen on.
Is there a particular reason for not implementing those surface terms in IGA, like a technical difficulty that I am not yet aware of? Otherwise, could you give me insights into where to start if I were to implement my own quadrature rule for computing surface integrals in IGA mode? I haven't figured out in which module the evaluation of Bernstein basis functions at Gauss quadrature points occurs. I know juggling with NURBS, Bézier meshes, etc. doesn't seem particularly easy. Yet I'm willing to give it a try.
Thank you very much for your help. Best regards,
Hugo L.
[1] T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2005, 194 (39-41), pp.4135-4195. 10.1016/j.cma.2004.10.008. hal-01513346
[2] Cimrman, Robert. (2014). Enhancing SfePy with Isogeometric Analysis.
[3] Michael J. Borden, Michael A. Scott, John A. Evans, Thomas J. R. Hughes: Isogeometric finite element data structures based on Bezier extraction of NURBS, Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, March 2010.