非绝缘超导扁平螺线管充电模型直接和迭代求解器的可扩展性分析
Scalability Analysis of Direct and Iterative Solvers Used to Model Charging of Non-insulated Superconducting Pancake Solenoids
摘要：
本文提出了一种非绝缘超导扁平管充电模拟的数学模型。通过在Petra-M FEM平台上使用各种求解器实现的仿真模型获得数值解。一个可扩展性分析进行直接和预处理的迭代求解器为四个不同的煎饼与不同数量的匝数和网格元素。据发现，即使有两个非常不同的时间尺度在系统中的迭代求解器组合（FGMRES-GMRES）与并行辅助空间麦克斯韦求解器（AMS）预处理优于并行直接求解器（MUMPS）。在一般情况下，迭代求解器的计算时间被发现增加的匝数在超导材料和/或假设的电导率。
英文摘要：
A mathematical model for the charging simulation of non-insulated superconducting pancake solenoids is presented. Numerical solutions are obtained by the simulation model implemented on the Petra-M FEM platform using a variety of solvers. A scalability analysis is performed for both direct and preconditioned iterative solvers for four different pancakes solenoids with a varying number of turns and mesh elements. It is found that even with two extremely different time scales in the system an iterative solver combination (FGMRES-GMRES) in conjunction with the parallel Auxiliary Space Maxwell Solver (AMS) preconditioner outperforms a parallelized direct solver (MUMPS). In general, the computational time of the iterative solver is found to increase with the number of turns in the solenoids and/or the conductivity assumed for the superconducting material.
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