电磁散射问题的隐式频域有限体积方法

Implicit frequency-domain finite volume 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的拓展,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)数计算显示了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 novel implicit frequency-domain finite volume method for directly solving the scattered-field formulation of frequency-domain Maxwell’s equations is proposed to obtain the precise spatial distribution of electromagnetic fields and scattering characteristics of targets under harmonic wave incidence. This method is an extension of the time-domain finite volume method from temporal to spectral domains, transforming solution variables from real-valued 4D spacetime coordinates into complex-valued 3D spatial representations while enabling applications of various steady-state acceleration techniques. It is a semi-discrete scheme, whose solution process involves two steps: steady-state virtual time integration and implicit LU-SGS (lower upper symmetric Gauss Siedel) solving of the spatial flux residual. Calculations with Large Courant number show that this implicit algorithm has the advantage of unconditional stability. Numerical examples demonstrate that the frequency-domain finite volume method exhibits comparable computational accuracy to methods of the moments and Mie series solutions. It indicates that this method has extensive applicability across various scenarios.

     

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