Separated Representations and PGD-Based Model Reduction - Fundamentals and Applications

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.

List of contents

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.

Summary

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.

Product details

• Assisted by: Francisc Chinesta (Editor), Francisco Chinesta (Editor), Ladevèze (Editor), Ladevèze (Editor), Pierre Ladevèze (Editor)
• Publisher: Springer, Wien
• Languages: English
• Product format: Hardback
• Released: 30.09.2014
• EAN: 9783709117934
• ISBN: 978-3-7091-1793-4
• No. of pages: 227
• Dimensions: 160 mm x 240 mm x 18 mm
• Weight: 467 g
• Illustrations: VII, 227 p. 74 illus., 40 illus. in color.
• Series: CISM International Centre for Mechanical Sciences; International Centre for Mechanical Sciences; CISM International Centre for Mechanical Sciences
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; B, Computer-Aided Design (CAD), engineering, Civil Engineering, Theoretical and Applied Mechanics, Mechanics, Mechanics, Applied, Computer mathematics, Computational Science and Engineering, Maths for scientists, Computer-Aided Engineering (CAD, CAE) and Design, Computer-aided engineering