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On the variational formulation of hybrid finite element-boundary integral techniques for electromagnetic analysis

机译：电磁分析混合有限元边界积分技术的变分形式

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摘要

This paper addresses the time-harmonic, electromagnetic analysis of a three-dimensional inhomogeneous radiator/scatterer in free-space. Such analysis can be carried out by combining the finite element method (FEM) with the method of moments (MoM), which yields finite element-boundary integral (FE-BI) formulations. A general framework is presented, within which stationary FE-BI formulations can be established (variational boundary-value problems), which relate to equivalent, underlying variational principles (stationary functionals). The formulations are shown to be accurate, robust and computationally efficient. They avoid the problem of interior resonances without resorting to the combined field integral equation and they result in symmetric system matrices, which preserve reciprocity explicitly. Thus, the stationary FE-BI framework combines the FEM and MoM on the continuous level, as opposed to the usual approach of hybridization after discretization, which generally leads to asymmetric matrices. The stationary FE-BI framework allows one to solve either for the electric and magnetic fields on the volume of the problem domain, or for one volume and one exterior surface field quantity, with only marginal differences in computational cost. The volume-surface formulations have the same storage requirements as previous FE-BI formulations and can be more efficiently solved. The volume-volume formulations provide simultaneous solutions of the electric and magnetic fields, which could for instance be used to construct error estimators directly based on Maxwell's equations.
机译：本文讨论了自由空间中三维非均匀辐射体/散射体的时谐电磁分析。可以通过将有限元方法（FEM）与弯矩方法（MoM）相结合来进行这种分析，从而得出有限元边界积分（FE-BI）公式。提出了一个通用框架，可以在其中建立平稳的FE-BI公式（变量边界值问题），该公式与等效的基本变量原理（平稳功能）相关。所显示的公式是准确，可靠且计算有效的。它们避免了内部共振的问题，而无需诉诸组合场积分方程，并且它们导致对称的系统矩阵，从而明确保留了互易性。因此，固定的FE-BI框架在连续水平上结合了FEM和MoM，这与离散化后通常的杂交方法相反，后者通常会导致矩阵不对称。固定的FE-BI框架允许解决问题域体积上的电场和磁场，或者解决一个体积和一个外表面场量，而计算成本只有很小的差异。体积表面配方与以前的FE-BI配方具有相同的存储要求，可以更有效地解决。体积-体积公式可同时提供电场和磁场的解，例如可用于直接基于Maxwell方程构建误差估计器。

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