Orientation of the normal in 2D

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1

I would like to solve a scattering problem in 2D. The scatterer is a subdomain for example:

def square(hmax=0.1,pml_rad=2,delta_pml=1):
geo = SplineGeometry()
L2=.5
geo.AddRectangle(p1=(-L2,-L2),p2=(L2,L2),bc=“trans”,leftdomain=3,rightdomain=1)
geo.AddCircle( (0,0),pml_rad+delta_pml , leftdomain=2, rightdomain=0, bc=“outerbnd”)
geo.AddCircle( (0,0), pml_rad, leftdomain=1, rightdomain=2)
geo.SetMaterial(1, “air”)
geo.SetMaterial(2, “PML”)
geo.SetMaterial(3, “scatterer”)
mesh = Mesh(geo.GenerateMesh(maxh=hmax))
return(mesh,pml_rad,ngmesh)

I get the normal via

nv=specialcf.normal(mesh.dim)

Is there some way to test that the normal in nv is outwards from the scatterer (so I can set transmission conditions), and reverse the normal if needed?

Thanks in advance for your help.

Best
Peter

2

Hi Peter,

you can visualize the normal vector by interpolating it into a VectorH1 GridFunction, e.g.

mesh, pml, ngmesh = square()

gfnv = GridFunction(VectorH1(mesh,order=1))
gfnv.Set(specialcf.normal(2),definedon=mesh.Boundaries(“.*”))
Draw(gfnv, mesh, “nv”)

In the Netgen GUI in Visual by enabling “Draw Surface Vectors” on the bottom right (and maybe increasing the Grid at the top left) the drawn arrows should show the direction of the normal vector. It looks like that in this example all normal vectors point outwards the whole domain.

Best,
Michael

3

Thanks for a very helpful response.
Peter