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3d_antiperiodic

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3d_antiperiodic   {  3D_ANTIPERIODIC.PDE

This example shows the use of FlexPDE in a 3D problem with azimuthal

anti-periodicity.

(See the example ANTIPERIODIC.PDE for notes on antiperiodic boundaries.)

In this problem we create a repeated 45-degree segment of a ring.

 }   title '3D AZIMUTHAL ANTIPERIODIC TEST'   coordinates cartesian3   Variables     u   definitions     k = 1     { angular size of the repeated segment: }     an = pi/4         { the sine and cosine for transformation }     crot = cos(an)       srot = sin(an)     H = 0     xc = 1.5     yc = 0.2     rc = 0.1   equations     u : div(K*grad(u)) + H = 0   extrusion z=0,0.4,0.6,1   boundaries     region 1 { this line forms the remote boundary for the later periodic statement }

start(1,0) line to (2,0)

value(u) = 0 arc(center=0,0) to (2*crot,2*srot)

{ The following line segment is periodic under an angular rotation.

The mapping expressions take each point on the line into a corresponding

point in the base line.  Note that although all the mapped y-coordinates

will be zero, we give the general expression so that the transformation

will be invertible. }

antiperiodic(x*crot+y*srot, -x*srot+y*crot)

line to (crot,srot)

value(u)=0

arc(center= 0,0) to close

limited region 2

layer 2 H = 1

start(xc-rc,0) line to (xc+rc,0) to (xc+rc,rc) to (xc-rc,rc) to close

limited region 3

layer 2 H = -1

start((xc-rc)*crot,(xc-rc)*srot)

line to ((xc+rc)*crot,(xc+rc)*srot)

to ((xc+rc)*crot+rc*srot,(xc+rc)*srot-rc*crot)

to ((xc-rc)*crot+rc*srot,(xc-rc)*srot-rc*crot) to close

monitors

grid(x,y,z)

contour(u) on z=0.1

contour(u) on z=0.5

contour(u) on z=0.9

plots

grid(x,y,z)

contour(u) on z=0.1        painted

contour(u) on z=0.5        painted

contour(u) on z=0.9        painted

end