Title: Numerically solving the relativistic Grad-Shafranov equation in Kerr spacetimes: Numerical techniques Show Chinese title

Title: 数值求解克尔时空中的相对论Grad-Shafranov方程：数值技术

Abstract: The study of the electrodynamics of static, axisymmetric and force-free Kerr magnetospheres relies vastly on solutions of the so called relativistic Grad-Shafranov equation (GSE). Different numerical approaches to the solution of the GSE have been introduced in the literature, but none of them has been fully assessed from the numerical point of view in terms of efficiency and quality of the solutions found. We present a generalization of these algorithms and give detailed background on the algorithmic implementation. We assess the numerical stability of the implemented algorithms and quantify the convergence of the presented methodology for the most established setups (split-monopole, paraboloidal, BH-disk, uniform). Show Chinese abstract

Abstract: 对静态、轴对称和无力的Kerr磁层电动力学的研究很大程度上依赖于所谓的相对论Grad-Shafranov方程（GSE）的解。 文献中已经提出了多种求解GSE的数值方法，但尚无任何一种方法从数值角度全面评估其效率和求解质量。 我们提出这些算法的推广，并详细介绍了算法实现的背景。 我们评估了所实现算法的数值稳定性，并量化了所提出方法在最成熟设置（分裂单极子、抛物面、黑洞-盘、均匀）中的收敛性。