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On some parallel preconditioned CG schemes
Preconditioning indefinite systems arising from mixed finite element
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algorithm analysis angles applied approach approximation Axelsson behaviour block bound boundary called choice coefficient computed condition condition number conjugate gradient method consider consistently ordered convergence corresponding couplings created DARE defined definition denote determined diagonal discretization dominance effective eigenvalue entries equations error estimate example exists factorization finite element formula function further give given graph grid hierarchical incomplete factorization increasing iterative methods leads Lemma linear systems matrix mesh modified incomplete newest vertex nodes Note obtained operations optimal parallel parameters performed points polynomial positive preconditioner preconditioning present problem procedure processors Proof properties reduced refer refinement regular relation Report respect satisfy scheme shown singular solution solving sparsity pattern spectral standard stencil steps strategy structure symmetric Table technique Theorem triangle University unknowns upper values vector