论文标题
基本方案，用于无条件稳定的隐式有限差分时间域方法
Fundamental Schemes for Efficient Unconditionally Stable Implicit Finite-Difference Time-Domain Methods
论文作者
论文摘要
本文介绍了基本方案的广义公式，用于无条件稳定的隐式有限差分时间域（FDTD）方法。基本方案构成了一个隐性方案家族，具有相似的基本更新结构，这些结构是最简单的，最有效的右侧。基本方案的表述是根据与某些经典分裂公式有关的广义矩阵操作方程式提出的，包括与隐式的交替方向，本地一维和分裂步骤方案。为了进一步了解基本方案的含义和意义，分析也扩展到了许多其他具有独特分裂公式的方案。详细的算法是为基于基本方案的无条件稳定隐式FDTD方法的新有效实现所描述的。对各种隐式方案进行了比较研究，在其原始和新实施中进行了比较，其中包括其计算成本和效率提高的比较。
This paper presents the generalized formulations of fundamental schemes for efficient unconditionally stable implicit finite-difference time-domain (FDTD) methods. The fundamental schemes constitute a family of implicit schemes that feature similar fundamental updating structures, which are in simplest forms with most efficient right-hand sides. The formulations of fundamental schemes are presented in terms of generalized matrix operator equations pertaining to some classical splitting formulae, including those of alternating direction implicit, locally one-dimensional and split-step schemes. To provide further insights into the implications and significance of fundamental schemes, the analyses are also extended to many other schemes with distinctive splitting formulae. Detailed algorithms are described for new efficient implementations of the unconditionally stable implicit FDTD methods based on the fundamental schemes. A comparative study of various implicit schemes in their original and new implementations is carried out, which includes comparisons of their computation costs and efficiency gains.
