Model reduction of parametrized systems. ([2017])

• Record Type: Book
• Further Information: Note: Peter Benner [and four others], editors.
• Editors: Benner, Peter
• Contents: 4 A Reduced Basis Method with an Exact Solution Certificate and Spatio-Parameter Adaptivity: Application to LinearElasticity4.1 Introduction; 4.2 Preliminaries; 4.2.1 Problem Statement; 4.2.2 Abstract Error Bounds: Energy Norm and Compliance Output; 4.3 Upper Bound of the Dual Norm of the Residual; 4.3.1 Bound Form; 4.3.2 Minimum-Bound Solutions and Approximations; 4.4 Stability Constant; 4.4.1 Transformation of the Stability Constant; 4.4.2 A Residual-Based Lower Bound of the Minimum Eigenvalue; 4.4.3 FE Approximation of Bounds of t(u) 4.4.4 Offline-Online Efficient SCM and RB Bounds of t(u)4.5 Error Bounds; 4.6 Spatio-Parameter Adaptation; 4.7 Numerical Results; 4.7.1 Problem Description; 4.7.2 Uniform Spatio-Parameter Refinement; 4.7.3 Spatio-Parameter Adaptive SCM and RB Refinement; References; 5 A Reduced Basis Method for Parameter Functions Using Wavelet Approximations; 5.1 Introduction; 5.2 Reduced Basis Method; 5.3 Space-Time Variational Formulation for Parabolic Problems; 5.4 Reduced Basis Method for Parameter Functions; 5.4.1 Using the Initial Value as Parameter in a Space-Time Setting Preface; Contents; About the Editors; 1 Two Ways to Treat Time in Reduced Basis Methods; 1.1 Introduction; 1.2 Variational Formulations of Parabolic Problems; 1.2.1 Semi-variational Formulation; 1.2.2 Space-Time Variational Formulation; 1.3 Parametrized Problems and the RBM; 1.4 Reduced Basis Methods with POD-Greedy; 1.5 Space-Time Reduced Basis Methods; 1.6 Numerical Results; 1.6.1 Data; 1.6.2 Results; 1.7 Conclusions; References; 2 Simultaneous Empirical Interpolation and Reduced Basis Method: Application to Non-linear Multi-Physics Problem; 2.1 Introduction 2.2 A Simultaneous EIM-RB Method2.2.1 Preliminaries; 2.2.1.1 Empirical Interpolation Method; 2.2.1.2 Reduced Basis Method; 2.2.2 ser Method; 2.2.2.1 Error Estimation; 2.2.2.2 Some ser Variants; 2.3 Numerical Experiments; 2.4 Application to Multi-Physics Model; 2.4.1 Electro-Thermal Model; 2.4.2 Application to Bitter Magnet; 2.4.3 Application to Polyhelix Magnet; 2.5 Conclusion; References; 3 A Certified Reduced Basis Approach for Parametrized Optimal Control Problems with Two-Sided Control Constraints; 3.1 Introduction; 3.2 General Problem Statement and Finite Element Discretization 3.2.1 Preliminaries3.2.2 Abstract Formulation of Linear-Quadratic Optimal Control Problems and the First-Order Optimality Conditions; 3.3 Reduced Basis Method for the Primal Problem; 3.3.1 Reduced Basis Approximation; 3.3.2 Primal Error Bound; 3.4 Slack Problem and the Primal-Slack Error Bound; 3.4.1 FE and RB Slack Problem; 3.4.2 Primal-Slack Error Bound; 3.5 Greedy Sampling Procedure; 3.6 Numerical Results: Graetz Flow with Parametrized Geometry and Lower and Upper Control Constraints; 3.7 Conclusions; References
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2017
• Extent: 1 online resource, ill
• Subjects: 511.3/4; Mathematics; Mathematical models; Mathematical optimization; Computational complexity; MATHEMATICS / General; Computational complexity; Mathematical models; Mathematical optimization; Computers -- Programming -- Algorithms; Mathematics -- Applied; Technology & Engineering -- Mechanical; Mathematics -- Differential Equations; Mathematical theory of computation; Maths for engineers; Mechanical engineering & materials; Differential calculus & equations; Computer science_xMathematics; Electronic data processing; Engineering mathematics; Materials; Differential equations, partial; Mathematics -- Counting & Numeration; Numerical analysis; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783319587868; 3319587862
• Related ISBNs: 3319587854; 9783319587851
• Notes: Note: Includes bibliographical referneces.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.