Structure-preserving mesh coupling based on the Buffa-Christiansen complex

TL;DR

This paper reviews mesh coupling techniques at nonconforming interfaces, emphasizing structure preservation of Maxwell's equations, and introduces a novel Buffa-Christiansen complex-based projection method for improved accuracy and stability.

Contribution

The paper introduces a new structure-preserving projection method using the Buffa-Christiansen complex, enhancing mesh coupling accuracy while maintaining the de Rham complex structure.

Findings

The Buffa-Christiansen complex-based method outperforms simple Whitney interpolation.

Structure preservation improves the stability of electromagnetic simulations.

Comparison shows the new method's advantages over existing approaches.

Abstract

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.