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Magnetic vector potential

  1. Jun 22, 2011 #1
    hi everybody
    i want to solve the wave equation of the magnetic vector potential numerically in x-y plane grid,
    curl curl A= µ J
    anyone can help me

    thanks in advance
  2. jcsd
  3. Jun 22, 2011 #2


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    Well first you should use the identity "curl squared = grad div - del squared": ∇ x (∇ x A) = ∇ ∇·A - ∇2 A. Then choose a gauge ∇·A = 0. You're left with Laplace's equation, which can be solved numerically.
  4. Jun 22, 2011 #3
    thanks, but i have another question , the reusltant equation will be ∇^2 A=-µ J, and A is a vector, not a scalar, this one is not Laplace , is Poisson, or
  5. Jun 22, 2011 #4
    because the A is a vector then must be put in links of the grid, not on the nodes, or?
  6. Jun 22, 2011 #5


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    But J is a vector too. Solve the vector components separately in Cartesian coordinates and you have three Laplacian equations.
  7. Jun 22, 2011 #6
    do you mean that
    ∇^2 Ax=Jx,
    ∇^2 Ay=Jy,
    ∇^2 Az=Jz,
    and Ax, Ay, Az lies on the grid nodes
  8. Jun 22, 2011 #7


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    As you wish, though there are a few ways to setup the grid for electromagnetics depending on the exact numerical procedure. For example, a common grid for FDTD, the Yee grid, will offset the electric and magnetic fields from the grid points. That may also be appropriate here if you wish to do a second order finite difference approach.
  9. Jun 22, 2011 #8
    please , can you show me some examples to discrization of the magentic field potential in x-y-z plan , if any one has a paper of chapter of book can help me. and which methods could be stable numerically
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