Hello,
I am trying to generate the lumped mass matrix by setting integration rules.
For a 2d surface mesh in 3d, the following code works well.
Code:
ir = IntegrationRule(points = [(0,0), (1,0), (0,1)], weights = [1/6, 1/6, 1/6] )
ds_lumping = ds(intrules = { TRIG : ir })
However, for a 1d curved mesh in 2d, I guess it should be
Code:
ir = IntegrationRule(points = [(0,0), (1,0)], weights = [1/2, 1/2] )
ds_lumping = ds(intrules = { TRIG : ir })
However, it does not work.
Here is my code. I hope that the final result is a diagonal matrix.
Code:
import netgen.gui
import netgen.meshing as ngm
from ngsolve import *
p = [[1,0,0],[1,1,0],[0,1,0],[0,0,0]]
nr = len(p)
mymesh= ngm.Mesh(dim=2)
pids = []
for i in range(nr):
pids.append (mymesh.Add (ngm.MeshPoint(ngm.Pnt(p[i]))))
idx = mymesh.AddRegion("material", dim=1)
for i in range(nr):
if i<nr-1:
mymesh.Add(ngm.Element1D([pids[i],pids[i+1]],index=idx))
else:
mymesh.Add(ngm.Element1D([pids[i],pids[0]],index=idx))
mesh = Mesh(mymesh)
fes = H1(mesh,order=1)
u,v = fes.TnT()
ir = IntegrationRule(points = [(0,0), (1,0)], weights = [1/2,1/2])
ds_lumping = ds(intrules = { TRIG : ir }, definedon=mesh.Boundaries("material"))
a = BilinearForm(fes)
a += u*v*ds_lumping
a.Assemble()
print(a.mat)
Thank you very much for your time in advance.
