We construct a compact fourth-order scheme, in space and time, for the time-dependent Maxwell's equations given as a first-order system on a staggered (Yee) grid. At each time step, we update the fields by solving positive definite second-order elliptic equations. We face the challenge of finding compatible boundary conditions for these elliptic equations while maintaining a compact stencil. The proposed scheme is compared computationally with a non-compact scheme and data-driven approach.

翻译：我们构造了一种在时空上均具有四阶精度的紧致格式，用于求解在交错（耶氏）网格上以初值形式给出的一阶时变麦克斯韦方程组。在每个时间步中，通过求解正定二阶椭圆方程对场量进行更新。我们面临的挑战在于：在保持紧致模板的同时，为这些椭圆方程寻找兼容的边界条件。通过计算对比，将该格式与非紧致格式及数据驱动方法进行了比较。