## Preprint 2021-28

## Ana Alonso-Rodriguez, Jessika Camaño:

### A graph-based algorithm for the approximation of the spectrum of the curl operator

### Abstract:

We analyze a new algorithm for the finite element approximation of a family of eigenvalue problems for the curl operator that includes, in particular, the approximation of the helicity of a bounded domain. It exploits a tree-cotree decomposition of the graph relating the degrees of freedom of the Lagrangian finite elements and those of the first family of Nédélec finite elements to reduce significantly the dimension of the algebraic eigenvalue problem to be solved. The algorithm is well-adapted to domains of general topology. Numerical experiments, including a non simply connected domain with non connected boundary, are presented in order to assess the performance and generality of the method.

This preprint gave rise to the following definitive publication(s):

**Ana ALONSO-RODRIGUEZ, Jessika CAMAñO: ***A graph-based algorithm for the approximation of the spectrum of the curl operator*. SIAM Journal on Scientific Computing, vol. 45, 1, pp. A147-A169, (2023).