### 6.5 Boundary-element methods

The boundary-element method was developed by Yan and Sakurai (2000) and requires the magnetic
field vector and the -distribution on the boundary as input. The NLFFF equations relate the magnetic
field values on the boundary with those in the volume:
with for points in the volume and for boundary points and is the magnetic field
vector on the boundary, where
and are implicitly computed with integrals over the 3D volume,
The boundary-element method is slow for computing the NLFFF in a 3D domain. Rudenko and Myshyakov
(2009) raised questions on this method.