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Truncated Newton-Based Multigrid Algorithm for Centroidal Voronoi Diagram Calculation

Numerical Mathematics(Theory,methods and Applications) 2012年第2期5卷 242-259页

作者： Zichao Di Maria Emelianenko Stephen Nash Department of Mathematical Sciences George Mason UniversityFairfaxVA 22030USA. Systems Engineering and Operations Research Department George Mason UniversityFairfaxVA 22030USA

In a variety of modern applications there arises a need to tessellate the domain into representative regions,called Voronoi cells.A particular type of such tessellations,called centroidal Voronoi tessellations or CVTs,are in big demand due to their optimality properties important for many applications.The availability of fast and reliable algorithms for their construction is crucial for their successful use in practical settings.This paper introduces a new multigrid algorithm for constructing CVTs that is based on the MG/Opt algorithm that was originally designed to solve large nonlinear optimization problems.Uniform convergence of the new method and its speedup comparing to existing techniques are demonstrated for linear and nonlinear densities for several 1d and 2d problems,and O(k)complexity estimation is provided for a problem with k generators.

关键词： Centroidal Voronoi tessellation optimal quantization truncated Newton method Lloyd’s algorithm multilevel method uniform convergence

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A UNIFIED FRAMEWORK FOR THE CONSTRUCTION OF VARIOUS ALGEBRAIC multilevel PRECONDITIONING methodS

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Acta Mathematicae Applicatae Sinica 1999年第2期15卷 132-143页

作者：白中治 Institute of Computational Mathematics and Scientific/Engineering Computing the Chinese Academy of Sciences Beijing China Faculty of Mathematics and Informatics the University of Nijmegen Nijmegen Netherlands

A framework for algebraic multilevel preconditioning methods is presented for solving largesparse systems of linear equations with symmetric positive definite coefficient matrices, whicharise in the discretization of second order elliptic boundary value problems by the finite elementmethod. This framework covers not only all known algebraic multilevel preconditioning methods,but yields also new ones. It is shown that all preconditioners within this framework have optimalorders of complexities for problems in two-dimensional (2-D) and three-dimensional(3-D) problemdomains, and their relative condition numbers are bounded uniformly with respect to the numbersof both the levels and the nodes.

关键词： multilevel method polynomial acceleration finite element method,optimal-order preconditioner

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Fast multilevel methods for Solving Ill-posed Problems

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Northeastern Mathematical Journal 2005年第2期21卷 131-134页

作者：陈仲英宋丽红马富明 DepartmentofScientificComputing ZhongshanUniversityGuangzhou510275 不详

1 Introduetion Many industrial and engineering applieations require numerieally solving ill-posed Problems. Regularization methods are employed to find approximate solutions of these problems.The choice of regularization

关键词： Ill-posed problem regularization method multilevel method

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