航天飞船返回舱进入大气层时由于气动加热形成等离子体屏蔽层，会干扰甚至阻断电磁波的传输，给航天飞船再入返回时的实时通信和再入测量造成困难。本文的研究目的是建立电磁波在等离子体中传播的数学模型，采用计算电磁学算法对其进行仿真，为研究等离子体屏蔽层提供理论依据。

采用时域间断伽辽金(DGTD)算法对电磁波与等离子体之间的相互作用展开研究，基于辛普森法则，提出了一种二阶双线性Z变换(BZT)的时间离散方案，推导了可以模拟电磁波在（非磁化/磁化）等离子体中传播的高阶算法。该算法采用区域分解技术将计算域分为若干子域，针对不同子域采用混合阶基函数对等离子体控制方程进行展开，再利用BZT方法得到电磁场的时域迭代公式。为了在有限空间内模拟无限区域，引入复坐标拉伸变换，分别构建适用于各向同性及各向异性介质的完美匹配层(PML)，用于截断对应的计算区域，最终形成一套完整的求解等离子体电磁传播问题的理论体系。

采用基于双线性Z变换的时域间断伽辽金(BZT-DGTD)算法分别对非磁化和磁化等离子体中电磁传播情况进行了仿真，并将仿真结果与商业软件对比。BZT-DGTD算法的平均相对误差分别为-24.91dB和-37.38dB。此外，数值算例的仿真结果与等离子体的物理性质表现出了良好的一致性，验证了算法的正确性。在高频情况下，BZT-DGTD算法展现出更好的稳定性，同时，该方法在相同仿真时间内可以采用更大的时间步长以减少计算时间，提升了本文算例90%左右的计算效率，验证了所提算法在计算效率上的优势,为解决实际等离子体的电磁问题提供了参考价值。

When the spacecraft's re-entry module enters the atmosphere, a plasma shielding layer is formed due to aerodynamic heating, which can interfere or even block the transmission of electromagnetic waves, making it difficult for real-time communication and re-entry measurements during re-entry and re-entry of the spacecraft. The purpose of this paper is to establish the mathematical model of electromagnetic wave propagation in plasma, and simulate it with computational electromagnetism algorithm, so as to provide a theoretical basis for the study of plasma shielding layer.

The Discontinuous Galerkin Time Domain(DGTD) algorithm was used to study the interaction between electromagnetic waves and plasma. Based on the Simpson rule, a second-order bilinear Z-transform (BZT) time discretization scheme was proposed, and a higher-order algorithm was derived to simulate the propagation of electromagnetic waves in (non magnetized/magnetized) plasma. This algorithm uses domain decomposition technology to divide the computational domain into several sub domains, and uses mixed order basis functions to expand the plasma control equation for different sub domains. Then, the BZT method is used to obtain the time-domain iterative formula of the electromagnetic field. In order to simulate infinite regions in finite space, complex coordinate stretching transformation is introduced to construct perfectly matched layers (PMLs) suitable for isotropic and anisotropic media, which are used to truncate the corresponding computational regions and ultimately form a complete solution system for plasma electromagnetic problems.

The Discontinuous Galerkin Time Domain algorithm based on the bilinear Z-transform (BZT-DGTD) is used to simulate the electromagnetic propagation in the unmagnetized and magnetized plasma respectively, and the simulation results are compared with the commercial software. The average relative errors of the BZT-DGTD algorithm are -24.91 dB and -37.38 dB, respectively. In addition, the simulation results of the numerical examples show good consistency with the physical properties of the plasma, verifying the correctness of the algorithm. In high-frequency situations, the BZT-DGTD algorithm exhibits better stability. At the same time, this method can use larger time steps within the same simulation time to reduce computational time, improving the computational efficiency of the example in this paper by about 90%. This verifies the superiority of the proposed algorithm in computational efficiency and provides reference value for solving practical electromagnetic problems in plasma.

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