Tree-cotree implicit condensation in magnetostatics

A tree-cotree decomposition of the graph associated with a finite-element m esh allows the implementation of a method which is equivalent to a mixed on e 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-Co tree Implicit Condensation). A possible preconditioning scheme for the resu lting linear system is presented and the effect of the choice of particular tree-cotree decompositions is discussed from the point of view of numerica l performance.