Titlebook: Numerical Methods and Applications; 6th International Co Todor Boyanov,Stefka Dimova,Geno Nikolov Conference proceedings 2007 Springer-Verl

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Weighted Iterative Operator-Splitting Methods: Stability-Theoryeal with advanced operator-splitting methods. They are based on weighted iterative operator-splitting methods and decouple complicate problems in simpler problems. The stability of the weighted splitting method is discussed and the efficiency of such methods. For the stiff-problems we present the A-

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Weighted Iterative Operator-Splitting Methods and Applications we develop a new class of weighted iterative operator splitting methods. We present applications to systems of linear ODEs, which might contain also stiff parameters. The benefit of the proposed method is demonstrated with regard to convergence results and comparison to analytical solutions. We pro

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Multilevel Preconditioning of 2D Rannacher-Turek FE Problems; Additive and Multiplicative Methodstization by Rannacher-Turek non-conforming rotated bilinear finite elements on quadrilaterals. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinement are not nested (in general). To handle this, a proper two-level basis is

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Multigrid–Based Optimal Shape and Topology Design in Magnetostaticstigrid preconditioning. In case of shape optimization, we apply a geometric multigrid preconditioner to eliminate the underlying state equation while the outer optimization loop is the sequential quadratic programming, which is done in the multilevel fashion as well. In case of topology optimization

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Generalized Aggregation-Based Multilevel Preconditioning of Crouzeix-Raviart FEM Elliptic Problemsbased on various multilevel extensions of two-level finite element methods (FEM), as was first shown in [5]. Thereby, the constant . in the so-called Cauchy-Bunyakowski-Schwarz (CBS) inequality, which is associated with the angle between the two subspaces obtained from a (recursive) two-level splitt

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