04029nam 22007095 450 991029975990332120200702175640.03-7091-1794-110.1007/978-3-7091-1794-1(CKB)3710000000228771(EBL)1966782(OCoLC)891384847(SSID)ssj0001354006(PQKBManifestationID)11773471(PQKBTitleCode)TC0001354006(PQKBWorkID)11322489(PQKB)11244055(MiAaPQ)EBC1966782(DE-He213)978-3-7091-1794-1(PPN)181353598(EXLCZ)99371000000022877120140902d2014 u| 0engur|n|---|||||txtccrSeparated Representations and PGD-Based Model Reduction[electronic resource] Fundamentals and Applications /edited by Francisco Chinesta, Pierre Ladevèze1st ed. 2014.Vienna :Springer Vienna :Imprint: Springer,2014.1 online resource (234 p.)CISM International Centre for Mechanical Sciences, Courses and Lectures,0254-1971 ;554Description based upon print version of record.3-7091-1793-3 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.CISM International Centre for Mechanical Sciences, Courses and Lectures,0254-1971 ;554MechanicsMechanics, AppliedComputer mathematicsComputer-aided engineeringTheoretical and Applied Mechanicshttps://scigraph.springernature.com/ontologies/product-market-codes/T15001Computational Science and Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/M14026Computer-Aided Engineering (CAD, CAE) and Designhttps://scigraph.springernature.com/ontologies/product-market-codes/I23044Mechanics.Mechanics, Applied.Computer mathematics.Computer-aided engineering.Theoretical and Applied Mechanics.Computational Science and Engineering.Computer-Aided Engineering (CAD, CAE) and Design.004620620.00420285620.1Chinesta Franciscoedthttp://id.loc.gov/vocabulary/relators/edtLadevèze Pierreedthttp://id.loc.gov/vocabulary/relators/edtBOOK9910299759903321Separated Representations and PGD-Based Model Reduction2204606UNINA