Method of Relative Magnetic Helicity Computation II: Boundary Conditions for the Vector Potentials

Abstract: We have proposed a method to calculate the relative magnetic helicity in a finite volume as given the magnetic field in the former paper (Yang et al. {\it Solar Physics}, {\bf 283}, 369, 2013). This method requires that the magnetic flux to be balanced on all the side boundaries of the considered volume. In this paper, we propose a scheme to obtain the vector potentials at the boundaries to remove the above restriction. We also used a theoretical model (Low and Lou, {\it Astrophys. J.} {\bf 352}, 343, 1990) to test our scheme.