Read Back Signals in Magnetic Recording - Research Group Fidler

Numerical Methods
Here A ij are 3× 3-submatrices
describing the interaction of the j-th tetrahedron of the
conductor model with the i-th node of the magnetic model. Thus the matrix A= ( A ) is a
( 3n) ( 3m)
× -Matrix, where n denotes the number of nodes of the magnetic model and m the
number of tetrahedrons in the conductor model. Usually the matrix A is fully populated and
requires a lot of memory. The multiplication with such a matrix is very time consuming. To
speed up the calculation and save memory an adaptive cross-approximation technique can be
used (see chapter 4.3). Unfortunately this technique needs a lot of memory when calculating
the approximation of the interaction matrix A for large magnetic and conductor models.
4.4.5 Hybrid FEM/BEM for Current Field
To overcome the storage problem we proposed an alternative way to calculate the magnetic
field in the magnetic model. Here we use a common mesh for the magnet and the conductor
model. Similar to the stray field calculation (see Section 2.5.2) we can reduce the interaction
matrix to a boundary interaction matrix.
Starting from Equation (2.29)
curl H = j, (4.49)
applying the curl-operator on both sides, and considering that div H = 0 lead to a Poisson
equation for each component of H.
Δ H =−curl
j (4.50)
with boundary condition (see Appendix B)
out in
∂H ∂H
− = n× j
∂n ∂n
∂V
. (4.51)
Now the magnetic field can be calculated quite similar to the stray field, described in Section
4.2. We split the magnetic field into two parts
H = H1+ H 2,
(4.52)
where H 1 is the solution of
Δ H =− j (4.53)
in
1 curl
ij
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