Construction and Application of a Stable Nodal Integration Method in Computational Electromagnetics on Tetrahedral Meshes

一種基於四面體網格的穩定節點積分方法在計算電磁學中的構建及應用

馮慧(Hui Feng) ； 崔向陽(Xiangyang Cui)

《中國機械工程學刊》 41卷5期 (2020/10) Pp. 627-637

摘要

This paper presents a stable nodal integration method (SNIM) to solve nonlinear magnetostatic and transient eddy current electromagnetic problems. A weakened weak formulation based on nodes is firstly considered, framing the so-called node-based smoothing domains. Secondly, the integration scheme of SNIM formulation is derived by constructing appropriate equivalent smoothing domains and temporary integration points. And then, the authors use the presented method to solve various benchmark problems to observe its properties adopting linear nodal tetrahedral meshes. The results show that the proposed approach is better in sense of accuracy than traditional finite element method, and the effectiveness and potentialities of SNIM for electromagnetic applications can be witnessed.

關鍵字

Stable nodal integration method ； Magnetostatic ； Transient eddy current ； Linear tetrahedral meshes

並列摘要

本論文提出了一種穩定節點積分方法（SNIM）用於解決非線性靜磁和瞬態電渦流問題。首先，建立基於節點的弱－弱形式方程，同時形成基於節點的光滑積分區域。然後，構建出等效的光滑區域和輔助積分點來得到SNIM方法的積分方案。接下來，作者將所提出的的方法用於求解多個電磁問題的標準算例來測試其在採用線性四面體網格時的實際效果。結果表明，所提方案較傳統有限元法精度更高，並且可以看出本文方法在電磁問題中的有效性及應用潛力。