Using integration scheme depending on element location etc

Question

Dear All

I have seen where to definie additional schemes in quadrature_schemes.py
However, I would like to understand whether the selection
of the scheme can be done on a element by element basis, depending
on where the singularities of the potential are etc.

regards

Moritz

Answer 1

from dolfin import *

mesh = UnitSquareMesh(1,1)
V = FunctionSpace(mesh, 'CG', 2)

cf = CellFunction('size_t', mesh)
cf.set_all(0)
cf[0] = 1 
dx = dx[cf]

u, v = TrialFunction(V), TestFunction(V)
# default rule
a = u*v*dx()
# form with default rule on 0 cells and, vertex rule on 1 cells
b = u*v*dx(0, {"quadrature_rule": "default"}) \
  + u*v*dx(1, {"quadrature_rule": "vertex"})

A, B = assemble(a), assemble(b)
print A.array() - B.array()

# now switch quadrature rules
cf.set_all(1)
cf[0] = 0
# form compilation is not required again
B = assemble(b)
print A.array() - B.array()

Form b uses distinct quadrature rules according to value of cell function cf. Your adaptivity comes into play by setting values of cf according to your needs.

Comments

Dear Jan

Thanks a lot
This is very useful advice.
I thus need to add another 4 schemes, depending on whcih corner
of the tet sits on the nucleus and
iterate over the cells and check set the scheme
accordingly

Great

regards

Moritz