论文标题
为开发三维SBP-SAT FDTD方法：理论与验证
Towards the Development of A Three-Dimensional SBP-SAT FDTD Method: Theory and Validation
论文作者
论文摘要
为了增强传统有限差异时间域（FDTD）方法的可伸缩性和性能，开发了同时逐个近似项（SBP-SAT）FDTD方法的三维求和方法来解决复杂的电磁问题。它在理论上是稳定的，可以进一步用于具有不同网格尺寸的多个网格块。本文主要关注其三维实现的基本理论方面，用于各种边界条件的SAT以及数值分散属性以及与FDTD方法的比较。提出的SBP-SAT FDTD方法继承了FDTD方法的所有优点，该方法是无基质，易于实现的，并且具有相同的准确性，并且具有可忽略的运行时开销（0.13 \％）和内存使用情况（1.2 \％）。进行了四个数值示例，以验证该方法的有效性。
To enhance the scalability and performance of the traditional finite-difference time-domain (FDTD) methods, a three-dimensional summation-by-parts simultaneous approximation term (SBP-SAT) FDTD method is developed to solve complex electromagnetic problems. It is theoretically stable and can be further used for multiple mesh blocks with different mesh sizes. This paper mainly focuses on the fundamental theoretical aspects upon its three-dimensional implementation, the SAT for various boundary conditions, and the numerical dispersion properties and the comparison with the FDTD method. The proposed SBP-SAT FDTD method inherits all the merits of the FDTD method, which is matrix-free, easy to implement, and has the same level of accuracy with a negligible overhead of runtime (0.13\%) and memory usage (1.2\%). Four numerical examples are carried out to validate the effectiveness of the proposed method.
