Balloon Boundary

Inside 2D Extractor, three layers of increasingly large triangles surrounding the problem region are created, as shown below:

On the outer surface of this "balloon" region, a zero-total-charge boundary condition is imposed for CG solutions. That is, the integral (over the outer surface) of the normal component of the electric field is required to be zero. This integral is expressed in terms of the finite element DOFs and imposed as an additional constraint equation on the solution.

This prevents any net field lines from escaping from the drawn region to the outer boundary. Thus the outer boundary will not act like an additional ground.

For RL solutions, 2D Extractor imposes the condition Az = 0 (where Az is the z-component of the magnetic vector potential). This ensures there is no net current on the boundary, so it will not act as an additional current return path.