间断Galerkin方法及在电磁计算中的应用研究

项目名称： 间断Galerkin方法及在电磁计算中的应用研究

项目编号： No.11301057

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 李良

作者单位： 电子科技大学

项目金额： 22万元

中文摘要： 间断Galerkin(DG)方法在某种程度上可看成是有限体积法与有限元法的一种有机结合，兼具二者的优点。最近提出的杂交间断Galerkin(HDG)方法继承了DG方法的优点，且具有更少的全局自由度，因此期待HDG方法比经典DG方法效率更高。本项目将新型的HDG方法应用于频域电磁计算，进行相关理论和算法创新，以提高电磁模拟的精度和速度。主要研究内容包括：结合HDG离散的最优Schwarz算法；局部适定的HDG方法构造及其性能研究。实现最优Schwarz算法有两种途径：一是完全继承DG方法离散时的做法，不同之处只在于子区域内用HDG方法求解；二是将子区域间杂交项的连续性也考虑在内，即在子区域间交换电场和磁场相关信息的同时，也交换杂交项的信息。通过引入稳定项得到一类广泛的具有局部适定性与最优收敛性质的HDG方法。项目最终将形成一套求解复杂电磁环境下频域麦克斯韦方程的稳定、高效方法及软件包。

中文关键词： 杂交间断Galerkin方法；电磁计算；区域分解算法；局部适定性；高性能计算

英文摘要： Discontinuous Galerkin (DG) methods can be viewed as a clever combination of the finite element methods (FEM) and the finite volume methods (FVM). Ideally, the DG methods share almost all the advantages of the FEM and the FVM. Recently, hybridizable discontinuous Galerkin (HDG) methods have been introduced. Compared to the DG methods, the HDG methods have less globally coupled degrees of freedom. Thus, the HDG methods are considered to be computationally cheaper than the DG methods. This project will employ the newly introduced HDG methods to solve freqency-domain electromagnetic problems. The purpose of this project is to make the numerical modelling for the electromagnetic wave propagation in complex and heterogeneous media more accurate and faster. We shall consider the optimized Schwarz algorithm under the framework of the HDG methods as well as a class of locally well-posed HDG methods. There are two practical ways for the implementation of the optimized Schwarz methods. The First one is directly followed from the optimized Schwarz algorithm with DG discretization. Only the information of the electric field and magnetic field will be exchanged on the interfaces between subdomains in this case. The other one takes the continuity of the hybrid term into consideration besides the electric field and the magneti

英文关键词： Hybridizable discontinuous Galerkin method；electromagnetic computations；domain decomposition methods；local well-posedness；high performance computing