permanent_magnet

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permanent_magnet

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{ PERMANENT_MAGNET.PDE  

 

 This example demonstrates the implementation of permanant magnets in magnetic field problems.

 

 FlexPDE integrates second-order derivative terms by parts, which creates surface integral

 terms at cell boundaries.

 By including magnetization vectors inside the definition of H, these surface terms correctly

 model the effect of magnetization through jump terms at boundaries.

 If the magnetization terms are listed separately from H, they will be seen as piecewise

 constant in space, and their derivatives will be deleted.

 

 See the Electromagnetic Applications section for further discussion.

 

}  

 

Title 'A PERMANENT-MAGNET PROBLEM'  

 

Variables  

   A { z-component of Vector Magnetic Potential }  

 

Definitions  

   mu = 1

   S = 0             { current density }  

   Px = 0             { Magnetization components }  

   Py = 0  

   P = vector(Px,Py) { Magnetization vector }  

   H = (curl(A)-P)/mu { Magnetic field }    

   y0 = 8             { Size parameter }  

 

Materials

'Magnet' : Py = 10

'Other'  : mu = 5000

 

Initial values  

    A = 0  

 

Equations    

    A : curl(H) + S = 0  

 

Boundaries  

  Region 1  

    start(-40,0)  

    natural(A) = 0 line to (80,0)  

    value(A) = 0   line to (80,80) to (-40,80) to close  

 

  Region 2  

    use material 'Other'

    start(0,0)  

    line to (15,0) to (15,20) to (30,20) to (30,y0) to (40,y0) to (40,40)  

              to (0,40) to close  

 

  Region 3   { the permanent magnet }  

    use material 'Magnet'

    start (0,0) line to (15,0) to (15,10) to (0,10) to close  

 

Monitors  

  contour(A)  

 

Plots  

  grid(x,y)  

  vector(dy(A),-dx(A)) as 'FLUX DENSITY B'  

  vector((dy(A)-Px)/mu, (-dx(A)-Py)/mu) as 'MAGNETIC FIELD H'  

  contour(A) as 'Az MAGNETIC POTENTIAL'  

  surface(A) as 'Az MAGNETIC POTENTIAL'  

 

End