Substructuring the Hiptmair-Xu preconditioner for positive definite \(\textbf{H}(\varvec{curl},\Omega )\) problems

Considering positive \(\textbf{H}(\varvec{curl},\Omega )\) $\mathbf{H}(\mathit{curl},\mathrm{\Omega })$ problems, we propose a substructured version of the Hiptmair-Xu preconditioner based on a new formula that expresses the inverse of Schur systems in terms of the inverse matrix of the global volume problem.