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 bookAs 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.... AND F. TISSEUR, Detecting the causes of ill-conditioning in structural finite element models, Computers aamp; Structures, 133 (2014), pp. ... 77)  P. KNUPP AND K. SALARI, Verification of Computer Codes in Computational Science and Engineering, ... Metric and Normed Spaces, Graylock Press, Rochester, N.Y., 1957.
|Title||:||Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs|
|Author||:||Josef Malek, Zdenek Strakos|
|Publisher||:||SIAM - 2014-12-22|