Bases that vanish at the boundary

[mcurti]

Dear all,

I have a rather simple question or request for an example

Considering a unit square or a line with structured elements (for now), do you have an example where the basis functions, which could be splines or stds, for instance, and vanish at the boundary of the domain? Most probably I would have to remove some of the bases from the boundary elements, but I struggle to figure out what the syntax will look like.

Regards,
Mitrofan

[joostvanzwieten]

You can remove specific dofs from a basis (on a structured topology!) using parameter removedofs. The value should be a list of lists of dofs to exclude per dimension. Per dimension the first spline (dof 0) is non-zero at the left boundary and the last spline (dof -1) is non-zero at the right boundary. To remove all splines that are nonzero at the entire boundary, use [[0,-1]]*topo.ndims. Example:

from nutils import mesh
import numpy

topo, geom = mesh.rectilinear([4]*2)
basis = topo.basis('spline', degree=2, removedofs=[[0,-1]]*topo.ndims)

numpy.testing.assert_almost_equal(topo.boundary.sample('gauss', 0).eval(basis), 0)

The following examples also use removedofs: drivencavity.py and coil.py.