Preconditioning and the conjugate gradient method in the context of solving PDEs /

Preconditioning and the conjugate gradient method in the context of solving PDEs /

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Bibliographic Details
Author / Creator:Málek, Josef, author.
Imprint:Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2015.
Description:1 online resource (x, 104 pages)
Language:English
Series:SIAM spotlights ; 01
SIAM spotlights ; 01.
Subject:
Boundary value problems -- Numerical solutions.
Boundary value problems -- Numerical solutions
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/12577558
Hidden Bibliographic Details
Other authors / contributors:Strakoš, Zdeněk, author.
Society for Industrial and Applied Mathematics, publisher.
ISBN:9781611973846
1611973848
9781611973839
161197383X
Notes:Title from title screen, viewed 11/11/2014.
Includes bibliographical references and index.
English.
Summary:Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem. The book's central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together. This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.
Other form:Print version: 161197383X 9781611973839
Publisher's no.:SL01 SIAM
Table of Contents:
  • Preface
  • Introduction
  • Linear elliptic partial differential equations
  • Elements of functional analysis
  • Riesz map and operator preconditioning
  • Conjugate gradient method in Hilbert spaces
  • Finite-dimensional Hilbert spaces and the matrix formulation of the conjugate gradient method
  • Comments on the Galerkin discretization
  • Preconditioning of the algebraic system as transformation of the discretization basis
  • Fundamental theorem on discretization
  • Local and global information in discretization and in computation
  • Limits of the condition number-based descriptions
  • Inexact computations, a posteriori error analysis and stopping criteria
  • Summary and outlook
  • Bibliography
  • Index.

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