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On the optimality of an additive iterative refinement method by Maksymilian Dryja

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Published by Courant Institute of Mathematical Sciences, New York University in New York .
Written in English


Book details:

Edition Notes

Statementby Maksymilian Dryja, Olof B. Widlund.
ContributionsWidlund, Olof B.
The Physical Object
Pagination11 p.
Number of Pages11
ID Numbers
Open LibraryOL17866193M

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  Dryja, M. and Widlund, O.B. ( a), ‘On the optimality of an additive iterative refinement method’, in Proc. Fourth Copper Mountain Conf. on Multigrid Methods Cited by: Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems Article in Journal of Numerical Mathematics 18(1) April with 21 Reads. Publication Data. A general formulation of the additive correction methods of Poussin [4] and Watts [7] is presented. The methods are applied to the solution of finite difference equations resulting from elliptic and parabolic partial differential equations. A new method is developed for anisotropic and heterogeneous by: Abstract. Many parallel iterative algorithms for solving symmetric, positive definite problems proceed by solving in each iteration, a number of independent systems on subspaces. The convergence of such methods is determined by the spectrum of the sums of orthogonal projections on those subspaces, while the convergence of a related sequential method Cited by:

maximization methods and Fourier inversion. Certain topics in the book will be appropriate for an undergraduate class, but generally the book is aimed at a graduate-level audience. Some of the chapters end with a section devoted to exercises. In ad-dition, throughout the book there are . Taheri, A., Suresh, K."Adaptive w-refinement: a new paradigm in isogeometric analysis", Submitted to Computer Methods in Applied Mechanics and Engineering, January Kumar, T., Suresh, K." A density-and-strain based K-clustering approach to microstructural topology optimization", Struct Multidisc Op – (). conjugate gradient method and the DIRECT algorithm). We aim for clarity and brevity rather than complete generality and confine our scope to algorithms that are easy to implement (by the reader!) and understand. One consequence of this approach is that the algorithms in this book are often special cases of more general ones in the literature. The flowchart of the proposed method is shown in Fig. 1. First, in order to avoid very thin parts and isolated islands, small features of the topology optimization results are identified. Second, boundary refinement is executed along with characteristics preservation, in Cited by:

Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke-Jeeves, implicit filtering, MDS, and Nelder-Mead schemes in a unified by: 1. Introduction The fast adaptive composite grid method (FAC; cf. []) is a multilevel technique for efficient adaptive solution of partial differential equations. A fairly extensive convergence theory exists for FAC (cf. [2,,]), but with two exceptions Cited by: We propose iterative refinement techniques, as well as an adaptive reformulation of the quadratic problem, that can greatly reduce these errors without incurring high computational overheads. Numerical results illustrating the efficacy of the proposed approaches are : I M GouldNicholas, E HribarMary, NocedalJorge. Iterative refinement is an iterative method proposed by James H. Wilkinson to improve the accuracy of numerical solutions to systems of linear equations. When solving a linear system Ax = b, due to the presence of rounding errors, the computed solution x̂ may sometimes deviate from the exact solution x *.