Electromagnetics

{ PERMANENT_MAGNET.PDE  

This example demonstrates the implementation of permanent 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.

 }  

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