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co-normal value on a 1D surface segment

Guosheng Fu
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2 years 9 months ago #3846 by Guosheng Fu

co-normal value on a 1D surface segment was created by Guosheng Fu

Hello, I am trying to hack a co-normal value for 1D surface segment that is needed for a HDG formulation...
Basically, for each line segment on a 1D surface mesh (embedded in a 2D mesh), I want to assign value +1 or -1 to the two nodes of the segment based on its tangential direction.... any suggestion to hack this?
In the 2D surface case, we can do Cross(n, t), but it is not available in 1D.

Guosheng Fu
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2 years 9 months ago #3847 by Guosheng Fu

Replied by Guosheng Fu on topic co-normal value on a 1D surface segment

Well, I found a not so elegant solution based on orientation of the edge and a SurfaceL2 grid function...

Code:

gfn = GridFunction(Compress(SurfaceL2(mesh, order=1, definedon=mesh.Boundaries("interface"))))
    count = 0
    for e in mesh.Elements(BND):
        if e.mat=="interface":
            if e.vertices[0].nr > e.vertices[1].nr:
                gfn.vec[2*count+1] = 1
            else:
                gfn.vec[2*count+1] = -1 
            count += 1  

Guosheng Fu
Topic Author
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2 years 9 months ago #3848 by Guosheng Fu

Replied by Guosheng Fu on topic co-normal value on a 1D surface segment

Well, I found a not so elegant solution based on orientation of the edge and a SurfaceL2 grid function...

Code:

    gfn = GridFunction(Compress(SurfaceL2(mesh, order=1, definedon=mesh.Boundaries("interface"))))
    count = 0
    for e in mesh.Elements(BND):
        if e.mat=="interface":
            if e.vertices[0].nr > e.vertices[1].nr:
                gfn.vec[2*count+1] = 1
            else:
                gfn.vec[2*count+1] = -1 
            count += 1  

mneunteufel
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2 years 9 months ago #3849 by mneunteufel

Replied by mneunteufel on topic co-normal value on a 1D surface segment

Hi Guosheng,

for a 1D-surface in 2D you can use the specialcf.tangential function for the co-normal vector.

Code:

conormal = specialcf.tangential(2)

Best,
Michael

Guosheng Fu
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2 years 9 months ago #3850 by Guosheng Fu

Replied by Guosheng Fu on topic co-normal value on a 1D surface segment

Hi Michael,

Well, I want a hybrid mixed method on a 1D surface mesh, for this purpose, I need to have a co-normal on the nodes that changes signs when evaluated from neighboring segments.
Since there is no SurfaceHDiv space for 1D, currently, I am simply using SurfaceL2 space for the (scalar) velocity field, and evaluate the surface divergence as

Code:

grad(u).Trace()*t

where t is the tangential vector.
The term that is missing is the transmission condition that enforce back continuity of velocity

Code:

qhat*u*co_n*ds(element_boundary=True"interface")

where qhat is a H1-P1 (hybrid) space on the surface and u is the SurfaceL2 velocity space. You can see that, basically, I need the co-normal direction co_n that is like the normal constant in 1D mesh....
The previous snipt is a way to hack such a co-normal coefficient using P1-SurfaceL2, but I am not confident it will work for all meshes.
Any ideas?

Best,
Guosheng

mneunteufel
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2 years 9 months ago #3851 by mneunteufel

Replied by mneunteufel on topic co-normal value on a 1D surface segment

Hi Guosheng,

it is possible to imitate the HDivSurface by using an H1-space and equip it with the tangential vector. E.g. a lowest order HDivSurface could be achieved by

Code:

fesH = H1(mesh, order=1)
u,v = fesH.TnT()

con = specialcf.tangential(2)
u = u*con
v = v*con

Then, u and v are co-normal continuous functions on the mesh.

Another idea, similar to your code with the edge orientation, is to use two different specialcf.tangential vectors

Code:

nel   = specialcf.tangential()
nel_c = specialcf.tangential(consistent=True)

The second one does not change its sign depending from which element you are coming. Thus the product nel*nel_c will be 1 from the one and -1 from the other side. The consistent=True flag is rather new, but it should work also for 1D-surfaces.

Best,
Michael

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