摘要
用边有限元基函数导出了麦克斯韦 (Maxwell)方程的有限元关系式 ,计算了地下三维介质中磁偶极子的电磁场响应 .将场分量定义在有限单元的边上 ,解决了结点有限元方法中场切向分量不连续的矛盾 ,保证了源除外的所有单元内有旋无散的特性 .将总场分离成背景场和二次场 ,使该方法适用于任何方向的磁偶极子源 .通过模拟算例分析了 7种Krylov子空间迭代算法以及不完全乔累斯基分解预处理手段在解大型线性代数方程组中的计算效率和收敛特性 .对比结果表明 ,施加不完全乔累斯基分解作预处理的广义乘积型双共轭梯度算法GPBiCG (Pbicg)收敛最快 ,是三维复杂介质电磁响应数值模拟的首选算法 .
The finite element formulation of the Maxwell equation is derived by using the edge finite element method and is used to simulate the 3\|D electromagnetic responses to the subspace medium.Through the definition of the electric field in the edge of each cell,the problem of the discontinuity of the tangential components of the electric field between different cells in node finite element method is solved and this method also keeps the property of the non\|divergence and finite rotation.The separation of the total electric field into the background and the secondary fields makes it possible that the technique proposed in the paper is suitable for the magnetic dipole in any direction.The properties of the convergence of seven Krylov subspace iterative solvers and the effectiveness of the incomplete Cholesky decomposition pre\|conditioner are analyzed through two simulation examples.Comparisons of different solvers show that the generalized productive bi\|conjugate gradient iterative solver processed with pre\|conditioner has the best convergence and it is the best selection in 3\|D electromagnetic modeling. [
出处
《计算物理》
CSCD
北大核心
2002年第6期537-543,共7页
Chinese Journal of Computational Physics
基金
留学回国人员科研启动基金 (J0 2 0 1)
