简介：

简介：Westudypreconditioningtechniquesusedinconjunctionwiththeconjugategradientmethodforsolvingmulti-length-scalesymmetricpositivedefinitelinearsystemsoriginatingfromthequantumMonteCarlosimulationofelectroninteractionofcorrelatedmaterials.Existingpreconditioningtechniquesarenotdesignedtobeadaptivetovaryingnumericalpropertiesofthemulti-length-scalesystems.Inthispaper,weproposeahybridincompleteCholesky(HIC)preconditioneranddemonstrateitsadaptivitytothemulti-length-scalesystems.Inaddition,weproposeanextensionofthecompressedsparsecolumnwithrowaccess(CSCR)sparsematrixstorageformattoefficientlyaccommodatethedataaccesspatterntocomputetheHICpreconditioner.Weshowthatformoderatelycorrelatedmaterials,theHICpreconditionerachievestheoptimallinearscalingofthesimulation.Thedevelopmentofalinear-scalingpreconditionerforstronglycorrelatedmaterialsremainsanopentopic.