Tree-Cotree implicit condensation in magnetostatics

A tree-cotree decomposition of the graph associated with a finite-element mesh allows the implementation of a method which is equivalent to a mixed one but which gives rise to a symmetric positive definite linear system with a reduced number of unknowns. We will refer to this method as TCIC (Tree-Cotree Implicit Condensation). A possible preconditioning scheme for the resulting linear system is presented and the effect of the choice of particular tree-cotree decompositions is discussed from the point of view of numerical performance.