To avoid directly solving linear equations for major time marching in the finite element time-domain (FETD) method, the compressive sensing (CS) theory is introduced to construct an explicit iterative scheme instead of an implicit form. In this method, Whitney elements and a leapfrog model are applied to time-dependent Maxwell curl equations for space and time discretization. After a small number of iterations, steps for linear equations in the initial time, the electric field intensity and magnetic flux density are updated just by the linear combination of results of previous time steps. Furthermore, a restart mechanism is built to control the computational complexity and accuracy over a long simulation time. The effectiveness of the new algorithm is verified by analyzing 3-D resonant cavities.

中文翻译：

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一种改进的基于压缩感知的空腔问题快速有限元时域方法

为了避免在有限元时域 (FETD) 方法中直接求解主要时间推进的线性方程，引入了压缩感知 (CS) 理论来构建显式迭代方案而不是隐式形式。在这种方法中，惠特尼元素和蛙跳模型被应用于时间相关的麦克斯韦旋度方程，用于空间和时间离散化。经过少量迭代后，初始时间线性方程的步长、电场强度和磁通密度仅由前一时间步长结果的线性组合更新。此外，还建立了重启机制来控制长时间模拟的计算复杂性和准确性。通过分析 3-D 谐振腔验证了新算法的有效性。