基于Buffa-Christiansen复数的结构保持网格耦合
Structure-preserving mesh coupling based on the Buffa-Christiansen complex
AI总结：
本文探讨了非吻合界面网格耦合的最新进展，提出一种结构保持投影方法，利用Buffa-Christiansen复数选择Lagrange乘子空间，与Whitney和de Rham映射进行对比。
摘要：
本文综述了非吻合界面网格耦合的最新进展。网格耦合常用于电磁致动器和机器的建模与模拟。本文利用Whitney元提出主要思想，考虑了插值和投影方法。除了精度和效率外，强调方案是否保持de Rham复数的结构，这基础于麦克斯韦方程。作为新贡献，提出一种结构保持投影方法，其中Lagrange乘子空间选择自Buffa-Christiansen复数。其性能与基于Whitney和de Rham映射的直接插值方法以及Galerkin投影进行比较。
英文摘要：
The state of the art for mesh coupling at nonconforming interfaces is presented and reviewed. Mesh coupling is frequently applied to the modeling and simulation of motion in electromagnetic actuators and machines. The paper exploits Whitney elements to present the main ideas. Both interpolation- and projection-based methods are considered. In addition to accuracy and efficiency, we emphasize the question whether the schemes preserve the structure of the de Rham complex, which underlies Maxwell's equations. As a new contribution, a structure-preserving projection method is presented, in which Lagrange multiplier spaces are chosen from the Buffa-Christiansen complex. Its performance is compared with a straightforward interpolation based on Whitney and de Rham maps, and with Galerkin projection.
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