Preconditioning and the conjugate gradient method in the context of solving PDEs / Josef Málek, Zdeněk Strakoš, Charles University in Prague, Prague, Czech Republic.
- Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2015.
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1 PDF (x, 104 pages).
- Boundary value problems -- Numerical solutions.
- System Details:
- Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
- 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.
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
- Bibliographic Level Mode of Issuance: Monograph
Title from title screen, viewed 11/11/2014.
Includes bibliographical references and index.
- Strakoš, Zdeněk, author.
Society for Industrial and Applied Mathematics, publisher.
- Publisher Number:
- SL01 SIAM
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