基于无穷阶展开的一维麦克斯韦方程解析解
Analytical solutions of 1D Maxwell's equations via infinite-order expansions
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中文总结 AI 辅助
本研究采用无穷阶估计方案，给出一维麦克斯韦方程的闭式解析解，经案例验证可生成不同初值与源项配置下的精确解，为计算电磁学提供理论洞见与实用基准。
中文摘要 AI 辅助
麦克斯韦方程的解析解对理解电磁场的因果性与瞬时行为至关重要，但在具有一般初值和源项的开放空间场景中，这类解难以获取。本研究采用一种无穷阶估计方案，该方案可给出麦克斯韦方程的闭式解析解，其以一般的函数到函数变换形式表达，能直接将初值和源项映射为场量。多项案例研究展示了该方法，针对不同初值和源项配置得到了精确解，所得结果为计算电磁学提供了理论洞见与实用基准。
英文摘要
Analytical solutions to Maxwell's equations are essential for understanding the causal and instantaneous behavior of electromagnetic fields, yet they are challenging to obtain in open-space settings with general initial values and source terms. This work uses an infinite-order estimation scheme that yields closed-form analytical solutions to Maxwell's equations. The scheme is expressed as general function-to-function transformations that directly map initial values and source terms to the fields. Several case studies demonstrate the method, producing exact solutions for different initial and source configurations. The results provide both theoretical insight and practical benchmarks for computational electromagnetics.
