ABSTRACT

In order to further alleviate computational burdens and enhance accuracies, we propose an efficient amelioration on the complex-frequency-shifted perfectly matched layer (CFS- PML) via introducing both direct Z-transform (DZT) and matrix exponential (ME) methods for terminating the finite-difference time-domain (FDTD) region. The method is here referred as the DZT-ME-PML. Due to introducing the DZT method, the proposal can avoid the disadvantages of approximate bilinear and matched Z-transform in modeling fine and course structures, leading to achieving higher accuracies. Moreover, by employing the ME technique, the proposal develops into the compact first-order differential matrix form applied to evading the convolution manipulations, the variable replacements, and the formulation rearrangements during the mathematical derivations. Besides, the proposed DZT-ME-PML can not only flexibly terminate the arbitrary media when adding the DB constitutive relation, but efficiently attenuate evanescent waves, and reduce the late-time reflections due to the CFS scheme. Three-dimensional (3D) numerical examples have been carried out to illustrate the validity and accuracy of the proposed DZT-ME-PML. Eventually, applied to solving geophysical problem with the very low frequency (VLF) case, the DZT-ME-PML shows stronger absorption accuracy than the general ME-PML method.

摘要

为了进一步减轻计算负担并提高精度，我们通过引入直接Z变换（D Z T）和矩阵指数（ME）方法，提出了对复频移完美匹配层（CFS- PML）的一种有效改善措施用于终止时差有限域（FDTD）。该方法在此称为D Z T-ME-PML。由于引入了D Z T方法，因此该建议可以避免近似双线性和匹配Z的缺点。-转换精细和课程结构的建模，从而获得更高的精度。此外，通过采用ME技术，该建议发展为紧凑的一阶微分矩阵形式，可用于规避数学推导过程中的卷积运算，变量替换和公式重新排列。此外，提出的D Z T-ME-PML不仅可以在添加DB本构关系时灵活地终止任意介质，而且可以有效衰减e逝波，并减少CFS方案引起的后期反射。进行了三维（3D）数值示例来说明所提出的D Z的有效性和准确性 T-ME-PML。最终，D Z T-ME-PML应用于解决超低频（VLF）情况下的地球物理问题，比普通的ME-PML方法具有更强的吸收精度。