论文标题
分析Havriliak-Negami色散介质中Maxwell方程的向后欧拉型方案
Analysis of a Backward Euler-type Scheme for Maxwell's Equations in a Havriliak-Negami Dispersive Medium
论文作者
论文摘要
对于Havriliak-Negami（H-N）分散培养基中的Maxwell方程，相关的能量耗散定律尚未在连续水平和离散水平上解决。在本文中，我们严格地表明，H-N模型的能量可以由初始能量界定，并且该模型的体积良好。我们分析了向后的Euler型半混凝土方案，并证明了经过的离散能量会及时单调衰减。如此强大的稳定性可确保该方案无条件稳定。我们还引入了一种快速的时间卷积算法，以减轻涉及具有三个参数的Mittag-Leffler函数的奇异内核的极化关系中历史依赖的负担。我们提供了足够的数值结果，以通过二维的光谱 - 盖尔金方法来证明全盘式方案的效率和准确性。最后，我们考虑了复杂的相对介电常数和一些相关物理量的恢复中的有趣应用。
For the Maxwell's equations in a Havriliak-Negami (H-N) dispersive medium, the associated energy dissipation law has not been settled at both continuous level and discrete level. In this paper, we rigorously show that the energy of the H-N model can be bounded by the initial energy and the model is well-posed. We analyse a backward Euler-type semi-discrete scheme, and prove that the modified discrete energy decays monotonically in time. Such a strong stability ensures that the scheme is unconditionally stable. We also introduce a fast temporal convolution algorithm to alleviate the burden of the history dependence in the polarisation relation involving the singular kernel with the Mittag-Leffler function with three parameters. We provide ample numerical results to demonstrate the efficiency and accuracy of a full-discrete scheme via a spectra-Galerkin method in two dimensions. Finally, we consider an interesting application in the recovery of complex relative permittivity and some related physical quantities.
