Separated Representations and PGD-Based Model Reduction [electronic resource] : Fundamentals and Applications /
Chinesta, Francisco.editor.
Ladevèze, Pierre.editor.
The papers in this volume start with a description of  the construction of reduced models through a review of Proper Orthogonal Decomposition (POD) and reduced basis models, including their mathematical foundations and some challenging applications, then followed by a description of a  new generation of simulation strategies based on the use of separated representations (space-parameters, space-time, space-time-parameters, space-space,…), which have led to what is known as Proper Generalized Decomposition (PGD) techniques. The models can be enriched by treating parameters as additional coordinates, leading to fast and inexpensive online calculations based on richer offline parametric solutions. Separated representations are analyzed in detail in the course, from their mathematical foundations to their most spectacular applications. It is also shown how such an approximation could evolve into a new paradigm in computational science, enabling one to circumvent various computational issues in a vast array of applications in engineering science.
Description based upon print version of record.
Includes bibliographical references.
From the Contents: Model order reduction based on proper orthogonal decomposition: Model reduction: extracting relevant information -- Interpolation of reduced basis: a geometrical approach -- POD for non-linear models.
The papers in this volume start with a description of  the construction of reduced models through a review of Proper Orthogonal Decomposition (POD) and reduced basis models, including their mathematical foundations and some challenging applications, then followed by a description of a  new generation of simulation strategies based on the use of separated representations (space-parameters, space-time, space-time-parameters, space-space,…), which have led to what is known as Proper Generalized Decomposition (PGD) techniques. The models can be enriched by treating parameters as additional coordinates, leading to fast and inexpensive online calculations based on richer offline parametric solutions. Separated representations are analyzed in detail in the course, from their mathematical foundations to their most spectacular applications. It is also shown how such an approximation could evolve into a new paradigm in computational science, enabling one to circumvent various computational issues in a vast array of applications in engineering science.
Mechanics.
Mechanics, Applied.
Computer mathematics.
Computer-aided engineering.
Theoretical and Applied Mechanics.
Computational Science and Engineering.
Computer-Aided Engineering (CAD, CAE) and Design.