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

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4 years 4 months ago #2177 by BenWilson94
Projection of a high order solution on to the lowest order basis. was created by BenWilson94
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
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4 years 4 months ago #2178 by mneunteufel
Replied by mneunteufel on topic Projection of a high order solution on to the lowest order basis.
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

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( (x**2*y*(1-y),-y**3*x**2) ) ) #Interpolate high order solution to low order space gf_lo.Set(gf_ho)
also the high order functions will be locally projected yielding to a better approximation, see attached file.

Best,
Michael

File Attachment:

File Name: hcurl_proj...12-06.py
File Size:1 KB
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4 years 4 months ago #2181 by BenWilson94
Replied by BenWilson94 on topic Projection of a high order solution on to the lowest order basis.
Hi Michael,

That's excellent, thank you.

Kind regards,

Ben
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