瑕疵型网格的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Galerkin (discontinuous Galerkin, DG)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DG方法中,由于需要添加额外的稳定项,增加了算法复杂度,而近年来出现一种简化的DG(simplified DG, SDG)方法,该方法无需稳定项也可有效处理非共形网格,同时保持较好的计算精度。本文针对在非共形剖分中可能遭遇的网格剖分情况,系统地对瑕疵型网格进行分类,再进一步探究SDG方法处理不同瑕疵型网格的适应能力,评估瑕疵型网格对计算结果的影响,综合性地讨论了SDG在不同网格条件下的表现,为复杂工程目标的非共形网格建模与电磁散射精度评估提供参考。

         

        Abstract: In computational electromagnetics, the discontinuous Galerkin method is a widely adopted and effective approach for handling non-conformal meshes, offering significant flexibility in addressing challenges posed by complex geometries. Historically, the integral equation discontinuous Galerkin (IEDG) method required additional stabilization terms. increasing algorithmic complexity. Recently, a simplified discontinuous Galerkin (SDG) method has emerged that eliminates the need for stabilization terms while effectively processing non-conformal meshes and maintaining high computational accuracy. This study systematically classifies flawed non-conformal meshes encountered in non-conformal discretization scenarios. We further investigate the inherent mechanisms through which the SDG method processes various types of flawed non-conformal meshes, evaluate the impact of mesh imperfections on computational results, and comprehensively discuss SDG performance across varying mesh conditions, providing a reference for non-conformal grid modeling and electromagnetic scattering accuracy assessment of complex engineering targets.

         

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