Projection of a high order solution on to the lowest order basis.

Main Forum Old-Forum - do not post here
1

Hi,

I have a H(curl) finite element space solution computed for some order (say order=3) and would like to project this solution on to a low order discretisation for the same mesh, but with order =0 elements. I’m guessing this might be through the projector operator

Projector(mask, range) # mask: bit array; range: bool

Is this possible?

Thanks

Ben

2

Hi Ben,

yes, it is possible to use the projection operator. However, it just neglects the information about the high order functions

[code]gf_proj = GridFunction(fes_ho)

bt = BitArray(fes_ho.FreeDofs())
bt[:]=True
bt[mesh.nedge:] = False
P = Projector(bt, True)
gf_proj.vec.data = P*gf_ho.vec[/code]

If you use an HCurl space of order 0 and then use the Set method

[code]fes_ho = HCurl(mesh, order=3)
fes_lo = HCurl(mesh, order=0)

gf_ho = GridFunction(fes_ho)
gf_lo = GridFunction(fes_lo)

#Set something
gf_ho.Set( CoefficientFunction( (x2y(1-y),-y3*x**2) ) )

#Interpolate high order solution to low order space
gf_lo.Set(gf_ho)[/code]
also the high order functions will be locally projected yielding to a better approximation, see attached file.

Best,
Michael

https://ngsolve.org/media/kunena/attachments/889/hcurl_projection.py

Attachment: hcurl_projection_2019-12-06.py

3

Hi Michael,

That’s excellent, thank you.

Kind regards,

Ben