Dear Edouard,
Yes, in Newton-Cotes integration methods, some quadature points of the
regular grid correspond to vanishing weights and these points are indeed
eliminated. It would not be difficult to have an integration method with
the complete grid (this is an option of the add_point fonction of
getfem_integration.cc, in fact) but this is not available for the moment.
Best regards,
Yves
Le 16/01/2019 à 20:19, Edouard Oudet a écrit :
Dear all,
I studied a simple situation : a triangular mesh and defined a MeshIm
class based on Newton-Cotes methods of degree "degi". I expected for
every triangle to have (degi + 1) * (degi + 2) / 2 quadrature points.
Surprisingly for me, the following illustration below shows that for a
degree 4 for instance, I obtain 12 quadrature points which is
different from 15.. It seems that some vertices of the triangle are
not taken into account.
Is it because the weights of these points is 0.? Or perhaps I didn't
call the class in the right way?
Any comments are welcome,
best,
Edouard.
/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
import getfem
import numpy as np
def nb_imdata(degi):
# creation mesh / fem / im
NX = 6
tmesh = getfem.Mesh('regular_simplices', np.arange(0, 1 + 1. / NX,
1. / NX),
np.arange(0, 1 + 1. / NX,
1. / NX))
tmeshfem = getfem.MeshFem(tmesh, 1)
tmeshfem.set_fem(getfem.Fem('FEM_PK(2, 2)'))
tmeshim = getfem.MeshIm(tmesh, getfem.Integ('IM_NC(2,' + str(degi)
+ ')'))
#print tmeshim.im_nodes()
print 'degree ', degi, '|', \
'nb of quad points ', tmeshim.im_nodes(2)[0].shape[0], '|', \
'expected ', ((degi + 1) * (degi + 2) / 2)
for k in range(3, 10):
nb_imdata(k)
--
Yves Renard ([email protected]) tel : (33) 04.72.43.87.08
INSA-Lyon
20, rue Albert Einstein
69621 Villeurbanne Cedex, FRANCE
http://math.univ-lyon1.fr/~renard
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