Real Time Reduced Order Computational Mechanics : Parametric PDEs Worked Out Problems

• Record Nr.: UNINA9910864187803321
• Autore: Rozza Gianluigi
• Pubbl/distr/stampa: Cham : , : Springer, , 2024; ©2024
• ISBN: 3-031-49892-5
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (180 pages)
• Collana: SISSA Springer Series ; ; v.5
• Altri autori (Persone): BallarinFrancesco; ScandurraLeonardo; PichiFederico
• Disciplina: 620.10015118
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- 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.; Part 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.