LEADER 04517nam 22006975 450 001 9910254255803321 005 20251202121824.0 010 $a3-319-29994-8 024 7 $a10.1007/978-3-319-29994-5 035 $a(CKB)3710000000611079 035 $a(EBL)4428784 035 $a(SSID)ssj0001653790 035 $a(PQKBManifestationID)16432834 035 $a(PQKBTitleCode)TC0001653790 035 $a(PQKBWorkID)14982503 035 $a(PQKB)10716006 035 $a(DE-He213)978-3-319-29994-5 035 $a(MiAaPQ)EBC4428784 035 $a(PPN)192770446 035 $a(EXLCZ)993710000000611079 100 $a20160301d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aProper Generalized Decompositions $eAn Introduction to Computer Implementation with Matlab /$fby Elías Cueto, David González, Icíar Alfaro 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (103 p.) 225 1 $aSpringerBriefs in Applied Sciences and Technology,$x2191-5318 300 $aDescription based upon print version of record. 311 08$a3-319-29993-X 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- 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. . 330 $aThis book is intended to help researchers overcome the entrance barrier to Proper Generalized Decomposition (PGD), by providing a valuable tool to begin the programming task. Detailed Matlab Codes are included for every chapter in the book, in which the theory previously described is translated into practice. Examples include parametric problems, non-linear model order reduction and real-time simulation, among others. Proper Generalized Decomposition (PGD) is a method for numerical simulation in many fields of applied science and engineering. As a generalization of Proper Orthogonal Decomposition or Principal Component Analysis to an arbitrary number of dimensions, PGD is able to provide the analyst with very accurate solutions for problems defined in high dimensional spaces, parametric problems and even real-time simulation. . 410 0$aSpringerBriefs in Applied Sciences and Technology,$x2191-5318 606 $aMechanics, Applied 606 $aSolids 606 $aMathematics$xData processing 606 $aMathematical physics 606 $aSolid Mechanics 606 $aComputational Science and Engineering 606 $aTheoretical, Mathematical and Computational Physics 615 0$aMechanics, Applied. 615 0$aSolids. 615 0$aMathematics$xData processing. 615 0$aMathematical physics. 615 14$aSolid Mechanics. 615 24$aComputational Science and Engineering. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a518.2 700 $aCueto$b Eli?as$4aut$4http://id.loc.gov/vocabulary/relators/aut$00 702 $aGonza?lez$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aAlfaro$b Icíar$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254255803321 997 $aUNINA