论文标题
无界域中的时间依赖性麦克斯韦方程的无基质不连续的盖尔金方法
A matrix-free Discontinuous Galerkin method for the time dependent Maxwell equations in unbounded domains
论文作者
论文摘要
出现了无限域中3D时间依赖的麦克斯韦方程的不连续的Galerkin（DG）有限元方法（FEM）方法。该方法（在FEM库中实现）基于模态正交多项式基础的协变量转换，该基础最初定义在参考单纯性上。该方法导致一个明确的时间步进方案，将其倒置的质量矩阵最多是$ d \！\！\！d $ block-diagonal（在$ d \！= \！= \！2,3 $空间维度）中，矩阵将属于系统右侧的属性属性的矩阵分配为小参照元素的属性，与unmerix的属性不同。此外，我们表明，当通过基于复杂的拉伸方法的方法中包含未结合的域时，将保留引入的优化。
A Discontinuous Galerkin (DG) Finite Element Method (FEM) approach for the 3D time dependent Maxwell equations in unbounded domains is presented. The method (implemented in the FEM library NGsolve) is based on the covariant transformation of a modal orthogonal polynomial basis, originally defined on a reference simplex. The approach leads to an explicit time stepping scheme for which the mass matrix to be inverted is at most $d\!\times\!d$ block-diagonal (in $d\!=\!2,3$ spatial dimensions) while the matrix which discretizes the curl operators on the right-hand side of the system is a small reference matrix, independent from geometric properties of mesh elements. Furthermore, we show that the introduced optimizations are preserved when unbounded domains are also included in the formulation through a complex-stretching based approach.
