CAJ | 학술논문

该文阐述了Jacobian-free Newton-Krylov (JFNK)法的基本原理及其双端预处理形式的迭代格式，选择处于时变(非均匀)外磁场中的二维超导体为研究对象，建立了基于矢量磁位法的控制超导体电磁特性的偏微分方程及相关的非线性有限元矩阵方程和数值迭代策略。以时变外磁场中具有高尺寸比的超导薄带的交流损耗问题和永磁外场中块状高温超导体的磁悬浮问题为计算实例，在肯定计算程序有效性的基础上，检验了预处理JFNK法求解这2类典型问题时的计算性能，证实了预处理JFNK法能较为快速地求解大型超导非线性电磁场问题，可作为开发超导电磁场数值计算程序的优选方法。
해문천술료Jacobian-free Newton-Krylov (JFNK)법적기본원리급기쌍단예처리형식적질대격식，선택처우시변(비균균)외자장중적이유초도체위연구대상，건립료기우시량자위법적공제초도체전자특성적편미분방정급상관적비선성유한원구진방정화수치질대책략。이시변외자장중구유고척촌비적초도박대적교류손모문제화영자외장중괴상고온초도체적자현부문제위계산실례，재긍정계산정서유효성적기출상，검험료예처리JFNK법구해저2류전형문제시적계산성능，증실료예처리JFNK법능교위쾌속지구해대형초도비선성전자장문제，가작위개발초도전자장수치계산정서적우선방법。
The principal basis of the Jacobian-free Newton-Krylov (JFNK) algorithm was firstly introduced in conjunction with its iterative scheme using the split preconditioning technique, and then the partial differential equation with magnetic vector potential as the state variable for governing the electromagnetic properties of a 2-D superconductor (SC) subjected to time-varying/nonuniform magnetic fields was established, and the related nonlinear systems of finite element equations plus the adopted strategy for numerical iteration were released. Taking the ac loss problems of a high-aspect-ratio SC strip in a time-varying field and the maglev problems of a bulk high temperature superconductor (HTS) above a magnetic track as the studied cases, the computational performance of the preconditioned JFNK algorithm was tested on the basis of the validated program. It was found by this investigation that the preconditioned JFNK algorithm has the ability to rapidly solve the large nonlinear electromagnetic problems of SC, and is thus an advanced approach for developing the program to solve the electromagnetic problems of SC.