SphericalManifold and accuracy problem

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Praveen C

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Aug 10, 2016, 1:04:04 AM8/10/16
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Hello

I am trying the SphericalManifold in latest git version. I observe accuracy issues with this.

E.g., I compute surface area of sphere using degree k mapping and (k+1)-point GaussLobatto quadrature.

Unit sphere with 384 surface cells obtained from GridGenerator::hyper_sphere after 3 refinements

k=4
relative error in surface area = 8.77328e-09

k=6
relative error in surface area = 9.66812e-09

k=8
relative error in surface area = 1.12567e-08

As you see, there is no convergence in the area as I increase the degree.

Thanks
praveen

luca.heltai

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Aug 10, 2016, 4:02:24 AM8/10/16
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Dear Praven,

the issue seems to be the same as before, but we have not been able to pin point what the problem could be.

In particular, the problem is not in Manifold *per se*. It may be related to the way MappingQ and MappingQGeneric compute support points. I have verified that all quadrature points lie on the sphere (true), and that they have the correct ordering (true).

Manifold does not play any role after the support points have been computed, so I’m out of ideas on to why things should not work. This may be related to the introduction of MappingQGeneric, but I’m just shooting in the dark.

If you are willing to help, we could try to identify what the problem could be...

Bets,

Luca.
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Praveen C

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Aug 10, 2016, 4:44:51 AM8/10/16
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Dear Luca

I can try to look into it, but dont know where to begin. Give me some places where I should start looking. I suppose I should start with MappingQ and MappingQGeneric.

My shallow water project is stuck due to this, so I am really keen to resolve this issue.

Best
praveen

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luca.heltai

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Aug 10, 2016, 6:04:06 AM8/10/16
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Praven,

can we move the discussion to a gist (https://gist.github.com/)?

If you put your code there, we can start discussing some strategies.

Best,

Luca.
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