LEADER 04801nam 22004453 450 001 9910864187803321 005 20240526090246.0 010 $a3-031-49892-5 035 $a(MiAaPQ)EBC31353396 035 $a(Au-PeEL)EBL31353396 035 $a(CKB)32142952400041 035 $a(EXLCZ)9932142952400041 100 $a20240526d2024 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aReal Time Reduced Order Computational Mechanics $eParametric PDEs Worked Out Problems 205 $a1st ed. 210 1$aCham :$cSpringer,$d2024. 210 4$dİ2024. 215 $a1 online resource (180 pages) 225 1 $aSISSA Springer Series ;$vv.5 311 $a3-031-49891-7 327 $aIntro -- Preface -- Contents -- 1 A Short Introduction to Reduced Basis Method -- 1.1 Parametric PDEs -- 1.2 Reduced Basis Method -- Proper Orthogonal Decomposition (POD) -- Greedy Algorithm -- Affine Decomposition -- Speedup and Error Analysis -- 1.3 Beyond the Basics -- Supremizer -- Geometrical Parametrization -- Time-Dependent Problem -- Primal-Dual Approximation -- Successive Constraint Method (SCM) -- Empirical Interpolation Method (EIM) -- Discrete Empirical Interpolation Method (DEIM) -- References -- Part I Worked Out Problems for Beginners: Steady Cases -- 2 Worked Out Problem 1: Steady Heat Conduction in a Thermal Block -- 2.1 Problem Description -- 2.2 Numerical Results -- 2.3 Exercises -- References -- 3 Worked Out Problem 2: A Linear Elasticity Problem on a Square -- 3.1 Problem Description -- 3.2 Numerical Results -- 3.3 Exercises -- References -- 4 Worked Out Problem 3: Thermal Transfer Problem in a Parametrized Geometry -- 4.1 Problem Description -- 4.2 Numerical Results -- 4.3 Exercises -- References -- 5 Worked Out Problem 4: A Transport Problem for the 2D Graetz Flow -- 5.1 Problem Description -- 5.2 Numerical Results -- 5.3 Exercises -- References -- 6 Worked Out Problem 5: Heat Conduction with Gaussian Flux -- 6.1 Problem Description -- 6.2 Numerical Results -- 6.3 Exercises -- References -- Part II Advanced Worked Out Problems: Time Dependent and Nonlinear Cases -- 7 Worked Out Problem 6: Unsteady Heat Conduction in a Thermal Block -- 7.1 Problem Description -- 7.2 Numerical Results -- 7.3 Exercises -- References -- 8 Worked Out Problem 7: A Nonlinear Elliptic Problem -- 8.1 Problem Description -- 8.2 Numerical Results -- 8.3 Exercises -- References -- 9 Worked Out Problem 8: A Nonlinear Parabolic FitzHugh-Nagumo Problem -- 9.1 Problem Description -- 9.2 Numerical Results -- 9.3 Exercises -- References. 327 $aPart III Real-Life Worked Out Problems: Engineering Applications -- 10 Worked Out Problem 9: A Thermal Conduction Problem Through an Extended Surface -- 10.1 Problem Description -- 10.2 Numerical Results -- 10.3 Exercises -- References -- 11 Worked Out Problem 10: An Idealized Contact Problem in Linear Elasticity with Friction -- 11.1 Problem Description -- 11.2 Numerical Results -- 11.3 Exercises -- References -- 12 Worked Out Problem 11: A Linear Elasticity Application on a Beam Bridge -- 12.1 Problem Description -- 12.2 Numerical Results -- 12.3 Exercises -- References -- Part IV Fluid Dynamics Worked Out Problems -- 13 Worked Out Problem 12: Navier-Stokes System for a Backward-Facing Step -- 13.1 Problem Description -- 13.2 Numerical Results -- 13.3 Exercises -- References -- 14 Worked Out Problem 13: Bifurcating Coanda Effect in a Channel -- 14.1 Problem Description -- 14.2 Numerical Results -- 14.3 Exercises -- References -- 15 Worked Out Problem 14: Unsteady Navier-Stokes Equations for Vortex Shedding Behind a Cylinder -- 15.1 Problem Description -- 15.2 Numerical Results -- 15.3 Exercises -- References -- Part V More Advanced Worked Out Problems -- 16 Worked Out Problem 15: Stabilized Reduced Method for an Advection Dominated Problem -- 16.1 Problem Description -- 16.2 Numerical Results -- 16.3 Exercises -- References -- 17 Worked Out Problem 16: A Parametrized Elliptic Optimal Control Problem -- 17.1 Problem Description -- 17.2 Numerical Results -- 17.3 Exercises -- References -- 18 Worked Out Problem 17: Uncertainty Quantification for a Stochastic Thermal Block -- 18.1 Problem Description -- 18.2 Numerical Results -- 18.3 Exercises -- References. 410 0$aSISSA Springer Series 676 $a620.10015118 700 $aRozza$b Gianluigi$0755859 701 $aBallarin$b Francesco$01740672 701 $aScandurra$b Leonardo$01740673 701 $aPichi$b Federico$01740674 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910864187803321 996 $aReal Time Reduced Order Computational Mechanics$94166443 997 $aUNINA