Less remarkable but still evident is a behavior that can be observed when applying homogeneous Neumann boundary conditions on the solution of the Laplace equation. If more space is between the boundary and the relevant configurations, the solution can eventually become more precise, when the infinity of the surrounding space is of relevance.

Boundary element methods [56,80] circumvent these difficulties, because the tesselation of the underlying space is only required on the boundaries. The surrounding of the boundary is assumed to be linear, homogeneous, and isotropic. In this case it is not necessary to tessellate the domain far distant from the actual places of interest, but only the boundary has to be tessellated. Therefore, quantities are only stored on topological elements on the boundary.

A feature which makes the application of boundary elements attractive to simulation is that boundary elements and finite elements can be coupled in a simple manner. A practical example of the boundary element method is shown in [12], where a superconductive quadrapole coil is simulated and the effects of the surroundings are explicitly considered.