Lecture Notes on Multigrid Methods

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The Lecture Notes are primarily based on a sequence of lectures given by the author while been a Fulbright scholar at 'St. Kliment Ohridski' University of Sofia, Sofia, Bulgaria during the winter semester of 2009-2010 academic year. The notes are somewhat expanded version of the actual one semester class he taught there. The material covered is slightly modified and adapted version of similar topics covered in the author's monograph 'Multilevel Block-Factorization Preconditioners' published in 2008 by Springer. The author tried to keep the notes as self-contained as possible. That is why the lecture notes begin with some basic introductory matrix-vector ... continued below

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PDF-file: 129 pages; size: 2.4 Mbytes

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Vassilevski, P S June 28, 2010.

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The Lecture Notes are primarily based on a sequence of lectures given by the author while been a Fulbright scholar at 'St. Kliment Ohridski' University of Sofia, Sofia, Bulgaria during the winter semester of 2009-2010 academic year. The notes are somewhat expanded version of the actual one semester class he taught there. The material covered is slightly modified and adapted version of similar topics covered in the author's monograph 'Multilevel Block-Factorization Preconditioners' published in 2008 by Springer. The author tried to keep the notes as self-contained as possible. That is why the lecture notes begin with some basic introductory matrix-vector linear algebra, numerical PDEs (finite element) facts emphasizing the relations between functions in finite dimensional spaces and their coefficient vectors and respective norms. Then, some additional facts on the implementation of finite elements based on relation tables using the popular compressed sparse row (CSR) format are given. Also, typical condition number estimates of stiffness and mass matrices, the global matrix assembly from local element matrices are given as well. Finally, some basic introductory facts about stationary iterative methods, such as Gauss-Seidel and its symmetrized version are presented. The introductory material ends up with the smoothing property of the classical iterative methods and the main definition of two-grid iterative methods. From here on, the second part of the notes begins which deals with the various aspects of the principal TG and the numerous versions of the MG cycles. At the end, in part III, we briefly introduce algebraic versions of MG referred to as AMG, focusing on classes of AMG specialized for finite element matrices.

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PDF-file: 129 pages; size: 2.4 Mbytes

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  • Report No.: LLNL-TR-439511
  • Grant Number: W-7405-ENG-48
  • DOI: 10.2172/983392 | External Link
  • Office of Scientific & Technical Information Report Number: 983392
  • Archival Resource Key: ark:/67531/metadc1013439

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  • June 28, 2010

Added to The UNT Digital Library

  • Oct. 14, 2017, 8:36 a.m.

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  • Oct. 27, 2017, 5:36 p.m.

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Vassilevski, P S. Lecture Notes on Multigrid Methods, report, June 28, 2010; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc1013439/: accessed September 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.