Manual adaptation

This is an example of how to manually remove vertices and refine edges. With this, we can also implement anisotropic refinement.

Grid creation

We use the horizontal grid file that contains an interface \(\Gamma = [0.25, 0.75] \times {0.5}\) embedded in a domain \(\Omega = [0,1]^2\).

from dune.grid import reader
from dune.mmesh import mmesh

from dune.fem.view import adaptiveLeafGridView as adaptive
from dune.fem import parameter, adapt
parameter.append( { "fem.adaptation.method": "callback" } )

dim = 2
file = "grids/horizontal.msh"

gridView  = adaptive( mmesh((reader.gmsh, file), dim) )
hgrid = gridView.hierarchicalGrid

Interpolating some high order function

First, we interpolate some high order function.

from ufl import *
from dune.fem.space import dglagrange as functionspace

space = functionspace(gridView, order=5)
x = SpatialCoordinate(space)

uh = space.interpolate( sin(100*x[0]), name="uh")
uh.plot()

Removing and inserting vertices

Then, we can insert and remove arbitrary vertices. We flag the vertices that should be removed and define points to be inserted within cells. Points inserted in cells will be connected to the all of the cell’s vertices. Afterwards, we simply call adapt.

from dune.common import FieldVector

for v in gridView.vertices:
    if (v.geometry.center - FieldVector([0.3, 0.3])).two_norm < 0.1:
        hgrid.removeVertex(v)

for e in gridView.elements:
    if (e.geometry.center - FieldVector([0.7, 0.7])).two_norm < 0.2:
        hgrid.insertVertexInCell( e.geometry.center )

adapt([uh])
uh.plot()

Refining edges

Another possibility to change the grid is to bisect specific edges. Hereby, we have to define an edge for bisection by a corresponding intersection’s index.

def myRefine():
    for e in gridView.elements:
        for i in gridView.intersections(e):
            if hgrid.isInterface(i):
                hgrid.refineEdge(e, i.indexInInside)

for i in range(5):
    myRefine()
    adapt([uh])

uh.plot()