A new method is proposed to solve Ampere's equation in an arbitrary toroidal domain in which all currents are known, given proper boundary conditions for the magnetic vector potential. The novelty of the approach lies in the application of singular value decomposition (SVD) techniques to tackle the difficulties caused by the kernel associated by the curl operator. This kernel originates physically due to the magnetic field gauge. To increase the efficiency of the solver, the problem is represented by means of a dual finite difference-spectral scheme in arbitrary generalized toroidal coordinates, which permits to take advantage of the block structure exhibited by the matrices that describe the discretized problem. The result is a fast and efficient solver, up to three times faster than the double-curl method in some cases, that provides an accurate solution of the differential form of Ampere law while guaranteeing a zero divergence of the resulting magnetic field down to machine precision.

提出了一种新方法，在给定矢量磁场势能的适当边界条件的情况下，在已知所有电流的任意环形域中求解安培方程。该方法的新颖之处在于奇异值分解（SVD）技术的应用，以解决由curl运算符关联的内核所造成的困难。该内核物理上归因于磁场计。为了提高求解器的效率，通过在任意广义环形坐标中的对偶有限差分谱方案表示问题，该方案允许利用描述离散问题的矩阵所展示的块结构。结果是一个快速高效的求解器，在某些情况下，其速度是双曲线方法的三倍，