论文标题
与时间相关的麦克斯韦方程式不连续的盖尔金离散化的后处理技术
A postprocessing technique for a discontinuous Galerkin discretization of time-dependent Maxwell's equations
论文作者
论文摘要
我们提出了一种新颖的后处理技术，用于不连续的Galerkin（DG）离散时间依赖时间的麦克斯韦方程，我们将其与明确的runge-kutta时间构建方案相对二。后处理的电磁场比在H（Curl） - norm中未加工的溶液快的订单速度快。提出的方法是局部的，从某种意义上说，增强的解决方案是在计算网格的每个单元格中独立计算的，并且在每个感兴趣的时间步骤中。结果，计算的价格很便宜，尤其是在关注区域本地化的情况下，无论是在时间还是空间上。这种后处理技术背后的关键思想源于可杂交的不连续的盖尔金（HDG）方法，该方法等同于被分析的DG方案，用于惩罚参数的特定选择。我们提出了几个数值实验，这些实验突出了后处理电磁场近似的超授权特性。
We present a novel postprocessing technique for a discontinuous Galerkin (DG) discretization of time-dependent Maxwell's equations that we couple with an explicit Runge-Kutta time-marching scheme. The postprocessed electromagnetic field converges one order faster than the unprocessed solution in the H(curl)-norm. The proposed approach is local, in the sense that the enhanced solution is computed independently in each cell of the computational mesh, and at each time step of interest. As a result, it is inexpensive to compute, especially if the region of interest is localized, either in time or space. The key ideas behind this postprocessing technique stem from hybridizable discontinuous Galerkin (HDG) methods, which are equivalent to the analyzed DG scheme for specific choices of penalization parameters. We present several numerical experiments that highlight the superconvergence properties of the postprocessed electromagnetic field approximation.
