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。但传统的DG方法中,由于需要添加额外的稳定项,增加了算法复杂度,近年来出现了一种简化的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,同时能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,先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。通过算例评估了瑕疵型网格对计算结果的影响,明确了SDG方法在不同瑕疵条件下的精度变化。本文综合性地讨论了SDG在不同网格条件下的表现,可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, and further investigates the adaptability of the SDG method to various types of flawed non-conformal meshes. The impact of mesh imperfections on computational results is evaluated from the illustrative example, and the accuracy variation of the SDG method under different flawed conditions is identified. The performance of SDG under varying mesh conditions is comprehensively discussed, providing a reference for non-conformal grid modeling and electromagnetic scattering accuracy assessment of complex engineering targets.

         

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