Very basic Isogeometric Analysis implementation in python/cython.
In order to learn about Isogeometric Analysis, Finite Element Analysis and NURBS, I rewrote a simplified version of geoPDEs (on sourceforge) using python as an exercise. The goal was to get it running quickly and not thinking too much about designing it in a pythonic way (it's not). If I'd do it again, it'd be completely different.
I'd like to express my gratitude to C. de Falco, A. Reali and R. Vazquezc for providing GeoPDEs.
Parts of the nurbs library is written is cython, hence it requires compiling.
cd into nrb/basis directory and execute:
python2 setup.py build_ext --inplace
cd ..
ln -s basis/bspline.so bspline.so
cd ..
e.g. very simple, coarse 2d Poisson problem, with just 8 degrees of freedom
$ python2 -O tests/laplace_2d_square_f_homDirichlet.py
Unknowns: 8 internal, 8 Dirichlet, 16 total.
Internal stiffness matrix
[[ 46.6667 -5.8333 -11.6667 -11.6667 0. 0. 0. 0. ]
[ -5.8333 46.6667 -11.6667 -11.6667 0. 0. 0. 0. ]
[-11.6667 -11.6667 93.3333 -11.6667 -11.6667 -11.6667 0. 0. ]
[-11.6667 -11.6667 -11.6667 93.3333 -11.6667 -11.6667 0. 0. ]
[ 0. 0. -11.6667 -11.6667 93.3333 -11.6667 -11.6667 -11.6667]
[ 0. 0. -11.6667 -11.6667 -11.6667 93.3333 -11.6667 -11.6667]
[ 0. 0. 0. 0. -11.6667 -11.6667 46.6667 -5.8333]
[ 0. 0. 0. 0. -11.6667 -11.6667 -5.8333 46.6667]]
Right hand side
[ 555.5556 555.5556 1111.1111 1111.1111 1111.1111 1111.1111 555.5556 555.5556]
Solution vector (including Dirichlet d.o.f):
[ 0. 31.746 31.746 0. 0. 31.746 31.746 0. 0. 31.746 31.746 0. 0. 31.746 31.746 0. ]
Sparse solution equals dense solution: True
*************** POST PROCESSING ******************
l2 error : 2.646
h1 error : 27.62
A matplotlib picture of the result will be shown interactively, and automatically saved as png.