Base functions and discrete constitutive relations for staggered polyhedral grids
Base functions and discrete constitutive relations for staggered polyhedral grids
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DOI：
10.1016/j.cma.2008.11.021
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发表时间：
2009-02
影响因子：
7.2
通讯作者：
L. Codecasa;R. Specogna;F. Trevisan
中科院分区：
文献类型：
--
作者：
L. Codecasa;R. Specogna;F. Trevisan
电磁问题可以根据离散几何方法（如有限积分法（FIT）或单元法（CM））在一对互锁的原始-对偶网格上离散化。然而，关键的方面是建设的离散对应的本构关系，确保稳定性和一致性的整体离散系统的代数方程。最初只考虑正交笛卡尔网格;最近可以处理四面体和三角形底斜棱柱的原始网格。本文提出了一套新的一般多面体原始网格的边和面矢量函数，符合精确的规格，允许构建稳定和一致的离散本构方程的框架内的一个充满活力的方法。
An electromagnetic problem can be discretized on a pair of interlocked primal–dual grids according to discrete geometric approaches like the Finite Integration Technique (FIT) or the Cell Method (CM). The critical aspect is however the construction of the discrete counterparts of the constitutive relations assuring stability and consistency of the overall discrete system of algebraic equations. Initially only orthogonal Cartesian grids where considered; more recently primal grids of tetrahedra and oblique prisms with triangular base can be handled. With this paper a novel set of edge and face vector functions for general polyhedral primal grids is presented, complying with precise specifications which allow to construct stable and consistent discrete constitutive equations in the framework of an energetic approach.