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Description:
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Elliptic partial differential equations that are used to model physical phenomena give rise to large sparse linear systems . Such systems can be symmetric positive definite and can be solved by the preconditioned conjugate gradients method . In this thesis , we develop support graph preconditioners for symmetric positive definite matrices that arise from the finite element discretization of elliptic partial differential 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 finite element matrices . |