Proper Generalized Decompositions : An Introduction to Computer Implementation with Matlab.

Intro -- Preface -- Acknowledgments -- Contents -- 1 Introduction -- 2 To Begin With: PGD for Poisson Problems -- 2.1 Introduction -- 2.2 The Poisson Problem -- 2.3 Matrix Structure of the Problem -- 2.4 Matlab Code for the Poisson Problem -- 3 Parametric Problems -- 3.1 A Particularly Challenging Problem: A Moving Load as a Parameter -- 3.2 The Problem Under the PGD Formalism -- 3.2.1 Computation of S(s) Assuming R(x) Is Known -- 3.2.2 Computation of R(x) Assuming S(s) Is Known -- 3.3 Matrix Structure of the Problem -- 3.4 Matlab Code for the Influence Line Problem -- 4 PGD for Non-linear Problems -- 4.1 Hyperelasticity -- 4.2 Matrix Structure of the Problem -- 4.2.1 Matrix Form of the Term T2 -- 4.2.2 Matrix Form of the Term T4 -- 4.2.3 Matrix Form of the Term T6 -- 4.2.4 Matrix Form for the Term T8 -- 4.2.5 Matrix Form of the Term T9 -- 4.2.6 Matrix Form of the Term T10 -- 4.2.7 Final Comments -- 4.3 Matlab Code -- 5 PGD for Dynamical Problems -- 5.1 Taking Initial Conditions as Parameters -- 5.2 Developing the Weak Form of the Problem -- 5.3 Matrix Form of the Problem -- 5.3.1 Time Integration of the Equations of Motion -- 5.3.2 Computing a Reduced-Order Basis for the Field of Initial Conditions -- 5.3.3 Projection of the Equations onto a Reduced, Parametric Basis -- 5.4 Matlab Code -- References -- Index.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.