Sarin, Vivek2005-02-172017-04-072005-02-172017-04-072004-122005-02-17http://hdl.handle.net/1969.1/1353Elliptic partial differential equations that are used to model physical phenomena give rise to large sparse linear systems. Such systems can be symmetric positive de?nite and can be solved by the preconditioned conjugate gradients method. In this thesis, we develop support graph preconditioners for symmetric positive de?nite matrices that arise from the ?nite element discretization of elliptic partial di?erential equations. An object oriented code is developed for the construction, integration and application of these preconditioners. Experimental results show that the advantages of support graph preconditioners are retained in the proposed extension to the ?nite element matrices.en-USpreconditioningconjugate gradients methodsupport theoryfinite element methodBook