Combinatorial preconditioners for scalar elliptic finite-element problems

We present a new preconditioner for linear systems arising from finite‐elements discretizations of scalar elliptic partial differential equations. The solver is based on building a symmetric diagonally dominant (SDD) approximation of the stiffness matrix K. The approximation is built by approximating each element inside the collection {Ke } of element matrices by an SDD matrix Le. The SDD approximation L is built by assembling the collection {Le }. We then sparsify L using a graph algorithm, and use the sparsified matrix as a preconditioner. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)