避免共能量的静磁学约化标量势方法
A reduced scalar potential approach for magnetostatics avoiding the coenergy
AI总结：
本文提出一种以磁标量势为主要未知量的静磁学方法，在保持矢量势形式所需较少牛顿迭代次数的同时，兼具标量势方法自由度少、实现简单的优势，并通过数值算例验证了其精度与效率提升。
摘要：
非线性静磁学问题的数值求解通常基于以磁势为变量的变分形式、有限元离散以及牛顿法等迭代求解器。矢量势方法旨在最小化某一能量泛函，在三维情形下需要使用棱边元并施加适当的规范条件。另一方面，标量势方法寻求最大化负共能量，并可通过标准拉格朗日有限元实现，从而减少自由度数量并简化实现。然而，据观察，求解主导非线性系统所需的牛顿迭代次数通常高于矢量势形式。本文提出一种结合两种方法优点的方法，即它需要与矢量势形式同样少的牛顿迭代次数，同时以磁标量势作为主要未知量。我们讨论该方法的变分背景、适定性及其高效实现。文中给出数值算例，以说明其精度以及与其他方法相比在效率上的提升。
英文摘要：
The numerical solution of problems in nonlinear magnetostatics is typically based on a variational formulation in terms of magnetic potentials, the discretization by finite elements, and iterative solvers like the Newton method. The vector potential approach aims at minimizing a certain energy functional and, in three dimensions, requires the use of edge elements and appropriate gauging conditions. The scalar potential approach, on the other hand, seeks to maximize the negative coenergy and can be realized by standard Lagrange finite elements, thus reducing the number of degrees of freedom and simplifying the implementation. The number of Newton iterations required to solve the governing nonlinear system, however, has been observed to be usually higher than for the vector potential formulation. In this paper, we propose a method that combines the advantages of both approaches, i.e., it requires as few Newton iterations as the vector potential formulation while involving the magnetic scalar potential as the primary unknown. We discuss the variational background of the method, its well-posedness, and its efficient implementation. Numerical examples are presented for illustration of the accuracy and the gain in efficiency compared to other approaches.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
