时域非连续伽略金（Discontinuous Galerkin Time Domain，DGTD）法作为近年来计算电磁学领域中的新型算法，因其精度高、便于并行等优点受到广泛关注。在电磁模拟中，由于单元级DGTD算法需要对整个计算区域采用相同的剖分类型和高精度的剖分尺寸来离散目标区域，这样会造成过多计算资源和时间成本的浪费。因此，降低资源消耗和提高计算效率在DGTD方法研究中具有重要的价值和意义。

本文针对多尺度复杂电磁模型求解难度高的问题，采用区域分解思想划分多个子域，根据精细程度选择不同网格剖分方式，同时采用混合阶基函数可以很好地减少资源消耗并提高计算效率。该方法采用EB和EH两种形式的麦克斯韦方程组作为控制方程，使用四面体和六面体两种网格进行剖分。结合区域分解方法构建两种形式的多域线性离散系统方程，将DGTD方法与适定PML(Well-posed PML)相结合来模拟无界问题。并给出了在PML区域中Maxwell方程组的矢量形式和相应的显式四阶龙格库塔时间迭代方法。同时该方法可以对PML域和物理域采取不同离散策略，也可以通过优化调整每个子域的剖分类型、剖分尺寸以及基函数的阶数来有效的降低自由度提高算法计算效率。将该算法应用于多尺度的电磁问题求解中，发现运用混合网格以及混合阶基函数的方法可以很好地提升仿真效率。仿真结果表明，在同等量级的计算精度情况下，采用子域级EB-DGTD相比于单元级DGTD方法内存消耗减少了87 %，自由度减少了96 %，时间成本降低99.7 %。

将EB-DGTD方法应用于电磁散射问题中，从圆极化波基础理论出发，结合总场散射场分离技术(TF/SF)提出了一种新的圆极化波注入方法，该方法将圆极化平面波完美注入计算域中，并进一步将单频圆极化扩展到宽频圆极化波。通过仿真发现，数值结果与解析解有着良好的一致性，同时也符合平面波的叠加原理，验证了算法的正确性。有效地解决了DGTD算法的圆极化波注入问题。为圆极化波在计算目标的RCS仿真研究中提供了理论参考。

The Discontinuous Galerkin Time Domain (DGTD) method, as a new algorithm in the field of computational electromagnetics in recent years, has received wide attention due to its advantages of high accuracy and ease of parallelism. Since the cell-level DGTD algorithm requires the same profile type and high-precision profile size for the whole computational region to discretize the target region, this will cause excessive computational resources and time cost wastage. Therefore, reducing resource consumption and improving computational efficiency are of great value and significance in the research of DGTD methods.

In this thesis, for the problem of high difficulty in solving multi-scale complex electro-magnetic models, we adopt the idea of area decomposition to divide multiple sub-domains, and choose different grid dissection methods according to the fineness, while using mixed-order basis functions can well reduce resource consumption and improve computational efficiency. The method adopts two forms of Maxwell's equations, EB and EH, as the controlling equations, and uses two types of meshes, tetrahedral and hexahedral, for dissection. The multi-domain linear discrete system equations of both forms are constructed by combining the region decomposition method, and the DGTD method is combined with the proper PML (Well-posed PML) to simulate the unbounded problem. And the vector form of Maxwell's system of equations in the PML region and the corresponding explicit fourth-order Longacurta time iteration method are given. Meanwhile, the method can adopt different discretization strategies for PML and physical domains, and also can improve the computational efficiency of the algorithm by optimally adjusting the dissection type, dissection size, and order of basis functions of each subdomain to effectively reduce the degrees of freedom. The algorithm is applied to the solution of multi-scale electromagnetic problems, and it is found that the efficiency of the simulation can be improved by using the hybrid grid and the hybrid order basis functions. The simulation results show that the subdomain-level EB-DGTD reduces the memory consumption by 87 %, the degrees of freedom by 96 %, and the time cost by 99.7 % compared with the cell-level DGTD method for the same magnitude of computational accuracy.

Applying the EB-DGTD method to the electromagnetic scattering problem, a new circularly polarized wave injection method is proposed from the fundamental theory of circularly polarized waves, combined with the total field scattering field separation technique (TF/SF), which perfectly injects circularly polarized plane waves into the computational domain and further extends the single-frequency circular polarization to bandwidth circularly polarized waves. Through simulation, it is found that the numerical results are in good agreement with the analytical solution and also conform to the superposition principle of plane waves, which verifies the correctness of the algorithm. The circularly polarized wave injection problem of the DGTD algorithm is effectively solved. It provides a theoretical reference for the study of circularly polarized waves in the RCS simulation of computational targets.

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