基于有限元的区域分解方法在永磁聚焦系统仿真中的应用

Application of Finite Element-Based Domain Decomposition Method to the Simulation for Permanent Magnet Focusing System

随着计算机技术以及并行求解技术的发展,区域分解方法越来越多地应用于计算电磁学的各个领域。针对微波管中的永磁聚焦系统仿真,该文提出一种基于有限元的非重叠区域分解方法,其引入一种新型传输条件,并采用内罚的方式推导出有限元弱形式。该区域分解法的最大优势是不需要引入多余的未知量,并且最终集成的有限元矩阵满足对称正定性,适合采用预处理共轭梯度法进行矩阵方程的求解。该文仿真了多个微波管永磁聚焦系统,并与商业软件Maxwell进行了详细的对比,结果表明所提出的区域分解方法和Maxwell精度相当,却拥有着更加优越的计算性能。

With the development of computer technology and parallel solving technology,domain decomposition method has been increasingly applied to various fields of computational electromagnetics.For the simulation of microwave tube permanent magnet focusing system,this paper proposes a finite element-based non-overlapping domain decomposition method,and introduces a novel transmission condition.Then the interior penalty formulation is used to derive the finite element weak form.The biggest advantage of the proposed domain decomposition method is that no extra unknowns are introduced,and the final finite element matrix is symmetric and positive definite,which makes the matrix equation suitable be solved by the preconditioned conjugate gradient method.In this paper,several microwave tube permanent magnet focusing systems are simulated and compared with the commercial software Maxwell in detail.The results show that the proposed domain decomposition method has the same accuracy as Maxwell,but has a more superior computational performance.