电磁散射问题的隐式频域有限体积方法

Implicit finite volume frequency domain method for electromagnetic scattering problems

  • 摘要: 为获得精确的电磁场空间分布和目标电磁散射特性,针对简谐波入射情况,提出了一种全新直接求解散射场形式频域麦克斯韦方程组的隐式有限体积方法。频域有限体积方法是时域有限体积方法从时域到频域拓展,待求解变量也从实数型时空四维转变到复数型空间三维变量,并可应用各种定常加速技巧。频域有限体积法半离散迭代求解过程包含定常虚拟时间推进和空间通量残差隐式LU-SGS求解两步骤。大库朗(CFL)数计算显示该全隐算法的无条件稳定性,二、三维完全导电体、介质、介质/导体混合目标以及复杂外形目标电磁散射的频域有限体积法结果与矩量法、Mie级数解等验证对比,证明该方法具有可信的计算精度和广泛的应用场景。

     

    Abstract: A new implicit finite volume frequency domain (FVFD) method for solving the Maxwell equations was proposed to accurately simulate the spatial distribution and scattering characteristic of electromagnetic fields for continuous incident wave. The FVFD is a natural extension of finite volume time domain (FVTD) method, in which the computational domain is transformed from time to frequency, and the variables are changed from real type to three-dimensional complex type. In the FVFD method, there are two semi-discrete iteration processes, stable pseudo time marching and LU-SGS implicit iteration of flux residual. Thus, acceleration techniques can be easily implemented into it. In the calculation, large Courant-Friedrichs-Lewyor (CFL) numbers can be adopted, which confirms its unconditional stable performance. The FVFD was used to simulate a series of canonical 2D and 3D perfect conductor, composite dielectric and complex shaped objects. The results agreed well with those simulated by method of moment (MOM) and Mie series, which demonstrated its high precision and extensive application scenarios of FVFD method.

     

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