A force-free field (FFF) is determined solely by the normal components of magnetic field and current density on the entire boundary of the domain. Methods employing three components of magnetic field suffer from overspecification of boundary conditions and/or a nonzero divergence-B problem. A vector potential formulation eliminates the latter issue, but introduces difficulties in imposing the normal component of current density at the boundary. This paper proposes four different boundary treatment methods within the vector potential formulation. We conduct a comparative analysis of the vector potential FFF solvers that we have developed incorporating these methods against other FFF codes in different magnetic field representations. Although the vector potential solvers with the new boundary treatments do not outperform our poloidal-toroidal formulation code, they demonstrate comparable or superior performance compared to the optimization code in SolarSoftWare. The methods developed here are expected to be readily applied not only to force-free field computations but also to time-dependent data-driven simulations.

본 논문에서는 고정 또는 자유 연단 조건의 모든 조합을 고려한 마름모꼴 평판의 휨 진동에 대한 엄밀한 해석방법을 제시한다. 본 논문의 주된 관점은 마름모꼴 평판 둔각 모서리의 경계조건이 고정 또는 자유일 때 휨응력의 특이도를 엄밀히 고려하여 해석하는 것이다. 고정 또는 자유인 모서리 응력 특이도의 중대한 영향력이 이해 될 수 있도록 충분히 큰 165º 둔각모서리를 갖는 마름모꼴 평판에 대하며 엄밀한 무차원 진동수와 수직 변동변위의 전형적인 등고선을 제시하였다.