Isogeometric Mortar Coupling for Electromagnetic Problems

TL;DR

This paper introduces and analyzes two domain decomposition methods for electromagnetic problems combining Nédélec finite elements and isogeometric analysis, demonstrating stability and implementation considerations.

Contribution

It presents a novel isogeometric mortar method and compares it with a modal basis approach, analyzing their stability and implementation for electromagnetic problems.

Findings

The new mortar method is unconditionally stable.

The mortar method leverages spline continuity for stability.

The modal basis approach is easier to implement but requires application knowledge.

Abstract

This paper discusses and analyses two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretised by either N\'ed\'elec-type polynomial finite elements or spline-based isogeometric analysis. The first approach is a new isogeometric mortar method and the second one is based on a modal basis for the Lagrange multiplier space, called state-space concatenation in the engineering literature. Spectral correctness and in particular inf-sup stability of both approaches are analytically and numerically investigated. The new mortar method is shown to be unconditionally stable. Its construction of the discrete Lagrange multiplier space takes advantage of the high continuity of splines, and does not have an analogue for N\'ed\'elec finite elements. On the other hand, the approach with modal basis is easier to implement but relies on application knowledge to ensure stability and correctness.