6.5 Boundary-element methods

The boundary-element method was developed by Yan and Sakurai (2000) and requires the magnetic field vector and the α-distribution on the boundary as input. The NLFFF equations relate the magnetic field values on the boundary with those in the volume:
∮ ( ) ∂B ∂¯Y ciBi = ¯Y ----− ---B0 dS (74 ) S ∂n ∂n
with ci = 1 for points in the volume and ci = 1∕2 for boundary points and B0 is the magnetic field vector on the boundary, where
( ) cos(λxr)- cos(λyr-)-cos(λzr)- ¯Y = diag 4πr , 4πr , 4πr (75 )
and λi(i = x,y, z) are implicitly computed with integrals over the 3D volume,
∫ Yi[λ2iBi − α2Bi − (∇ α × Bi)]dV = 0. (76 ) V
The boundary-element method is slow for computing the NLFFF in a 3D domain. Rudenko and Myshyakov (2009) raised questions on this method.
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