瑕疵型非共形网格的SDG方法适应性分析

      Adaptability analysis of SDG method for defect type nonconformal grids

      • 摘要: 在计算电磁学中,利用不连续伽辽金方法处理非共形网格是一种常用且有效的解决方法,它能够灵活应对复杂几何形状带来的挑战。传统的不连续伽辽金方法(IEDG)中,由于需要计算稳定项,对非共形网格的要求较高,现在出现一种简化的DG方法(SDG),无需稳定项也可以计算非共形网格,并保持较好的精度。本文首先对SDG的原理进行阐述;接着,针对在非共形剖分中可能遭遇的不同的网格剖分情况,明确定义非共形网格的类别,并给出具体的例子展示;再进一步探究不同的瑕疵型非共形网格与SDG方法之间的关系,评估其对计算结果的影响,综合性的讨论SDG在不同网格条件下的表现。

         

        Abstract: In computational electromagnetics, the discontinuous Galerkin (DG) method has been widely adopted as an effective approach for handling non-conformal meshes, demonstrating remarkable flexibility in addressing challenges posed by complex geometries. While traditional interior penalty discontinuous Galerkin (IEDG) methods impose stringent requirements on non-conformal meshes due to the necessity of computing stabilization terms, a simplified DG formulation (SDG) has recently emerged that eliminates stabilization terms while maintaining comparable accuracy in non-conformal mesh computations. This paper first elucidates the fundamental principles of the SDG method. Subsequently, it systematically categorizes various non-conformal mesh types encountered in practical partitioning scenarios through explicit definitions and illustrative examples. Furthermore, the study investigates the relationship between different defective non-conformal mesh configurations and SDG performance, quantitatively evaluates their impacts on computational results, and provides comprehensive discussions on SDG's behavior under diverse mesh conditions.

         

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