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Proper generalized decompositions[electronic resource] :an introduction to computer implementation with Matlab /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	518
書名/作者:	Proper generalized decompositions : an introduction to computer implementation with Matlab // by Elias Cueto, David Gonzalez, Iciar Alfaro.
作者:	Cueto, Elias.
其他作者:	Gonzalez, David.
出版者:	Cham : : Springer International Publishing :, 2016.
面頁冊數:	xii, 96 p. : : ill. (some col.), digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Decomposition (Mathematics)
標題:	Matrices.
標題:	Engineering.
標題:	Continuum Mechanics and Mechanics of Materials.
標題:	Computational Science and Engineering.
標題:	Numerical and Computational Physics.
ISBN:	9783319299945
ISBN:	9783319299938
內容註:	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.
摘要、提要註:	This book is intended to help researchers overcome the entrance barrier to Proper Generalized Decomposition (PGD), by providing a valuable tool to begin the programming task. Detailed Matlab Codes are included for every chapter in the book, in which the theory previously described is translated into practice. Examples include parametric problems, non-linear model order reduction and real-time simulation, among others. Proper Generalized Decomposition (PGD) is a method for numerical simulation in many fields of applied science and engineering. As a generalization of Proper Orthogonal Decomposition or Principal Component Analysis to an arbitrary number of dimensions, PGD is able to provide the analyst with very accurate solutions for problems defined in high dimensional spaces, parametric problems and even real-time simulation.
電子資源:	http://dx.doi.org/10.1007/978-3-319-29994-5

Proper generalized decompositions[electronic resource] :an introduction to computer implementation with Matlab /
Cueto, Elias.

Proper generalized decompositionsan introduction to computer implementation with Matlab /[electronic resource] :by Elias Cueto, David Gonzalez, Iciar Alfaro. - Cham :Springer International Publishing :2016. - xii, 96 p. :ill. (some col.), digital ;24 cm. - SpringerBriefs in applied sciences and technology,2191-530X. - SpringerBriefs in applied sciences and technology..

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.

This book is intended to help researchers overcome the entrance barrier to Proper Generalized Decomposition (PGD), by providing a valuable tool to begin the programming task. Detailed Matlab Codes are included for every chapter in the book, in which the theory previously described is translated into practice. Examples include parametric problems, non-linear model order reduction and real-time simulation, among others. Proper Generalized Decomposition (PGD) is a method for numerical simulation in many fields of applied science and engineering. As a generalization of Proper Orthogonal Decomposition or Principal Component Analysis to an arbitrary number of dimensions, PGD is able to provide the analyst with very accurate solutions for problems defined in high dimensional spaces, parametric problems and even real-time simulation.

ISBN: 9783319299945

Standard No.: 10.1007/978-3-319-29994-5doiSubjects--Uniform Titles:

MATLAB.
Subjects--Topical Terms:

590812
Decomposition (Mathematics)

LC Class. No.: QA402.2

Dewey Class. No.: 518

Proper generalized decompositions[electronic resource] :an introduction to computer implementation with Matlab /
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