论文标题
与时间相关的2D Maxwell方程的任意阶单细胞法具有块二基因质量肿瘤
An arbitrary-order Cell Method with block-diagonal mass-matrices for the time-dependent 2D Maxwell equations
论文作者
论文摘要
我们引入了一种新的数值方法，用于在两个空间维度中的非结构化网格上的时间依赖的麦克斯韦方程。这依赖于引入新的网格，该网格是起始Simplicial Mesh的Barycentric双重细胞复合物，以及在两个双重复合物的几何实体上近似两个未知字段。仔细的基础功能选择可为离散的时间稳定方案提供便宜的可逆块对基因系统矩阵。本贡献的主要新颖性在于将任意多项式度纳入通过新参考细胞定义的近似功能空间。提出的方法，尽管是一种不连续的Galerkin方法，但既不需要引入用户调整的罚款参数来进行田野的切向跳跃，也不需要数值耗散以实现稳定性。实际上，已证明了半二差异方案的精确电磁能源保护法，并在几个数值测试中显示，所得算法提供了带有预期收敛顺序的无虚拟溶液。
We introduce a new numerical method for the time-dependent Maxwell equations on unstructured meshes in two space dimensions. This relies on the introduction of a new mesh, which is the barycentric-dual cellular complex of the starting simplicial mesh, and on approximating two unknown fields with integral quantities on geometric entities of the two dual complexes. A careful choice of basis-functions yields cheaply invertible block-diagonal system matrices for the discrete time-stepping scheme. The main novelty of the present contribution lies in incorporating arbitrary polynomial degree in the approximating functional spaces, defined through a new reference cell. The presented method, albeit a kind of Discontinuous Galerkin approach, requires neither the introduction of user-tuned penalty parameters for the tangential jump of the fields, nor numerical dissipation to achieve stability. In fact an exact electromagnetic energy conservation law for the semi-discrete scheme is proved and it is shown on several numerical tests that the resulting algorithm provides spurious-free solutions with the expected order of convergence.
