Model reduction of complex dynamical systems / / Peter Benner [and five others]

• Pubblicazione: Cham, Switzerland : , : Springer International Publishing, , [2021]; ©2021
• Descrizione fisica: 1 online resource (416 pages)
• Disciplina: 309.173092
• Soggetto topico: System theory - History; Dynamics - Statistical methods; Teoria de sistemes; Dinàmica
• Soggetto genere / forma: Congressos; Llibres electrònics
• Persona (resp. second.): BennerPeter
• Nota di contenuto: Intro -- Preface -- Contents -- *-20pt Methods and Techniques of Model Order Reduction -- On Bilinear Time-Domain Identification and Reduction in the Loewner Framework -- 1 Introduction -- 1.1 Outline of the Paper -- 2 System Theory Preliminaries -- 2.1 Linear Systems -- 2.2 Nonlinear Systems -- 3 The Loewner Framework -- 3.1 The Loewner Matrix -- 3.2 Construction of Interpolants -- 4 The Special Case of Bilinear Systems -- 4.1 The Growing Exponential Approach -- 4.2 The Kernel Separation Method -- 4.3 Identification of the Matrix N -- 4.4 A Separation Strategy for the second Kernel -- 4.5 The Loewner-Volterra Algorithm for Time-Domain Bilinear Identification and Reduction -- 4.6 Computational Effort of the Proposed Method -- 5 Numerical Examples -- 6 Conclusion -- References -- Balanced Truncation for Parametric Linear Systems Using Interpolation of Gramians: A Comparison of Algebraic and Geometric Approaches -- 1 Introduction -- 2 Balanced Truncation for Parametric Linear Systems and Standard Interpolation -- 2.1 Balanced Truncation -- 2.2 Interpolation of Gramians for Parametric Model Order Reduction -- 2.3 Offline-Online Decomposition -- 3 Interpolation on the Manifold mathcalS+(k,n) -- 3.1 A Quotient Geometry of mathcalS+(k,n) -- 3.2 Curve and Surface Interpolation on Manifolds -- 4 Numerical Examples -- 4.1 A model for heat conduction in solid material -- 4.2 An Anemometer Model -- 5 Conclusion -- References -- Toward Fitting Structured Nonlinear Systems by Means of Dynamic Mode Decomposition -- 1 Introduction -- 2 Dynamic Mode Decomposition -- 2.1 Dynamic Mode Decomposition with Control (DMDc) -- 2.2 Input-Output Dynamic Mode Decomposition -- 3 The Proposed Extensions -- 3.1 Bilinear Systems -- 3.2 Quadratic-Bilinear Systems -- 4 Numerical Experiments -- 4.1 The Viscous Burgers' Equation -- 4.2 Coupled van der Pol Oscillators. ; 5 Conclusion -- 6 Appendix -- 6.1 Computation of the Reduced-Order Matrices for the Quadratic-Bilinear Case -- References -- Clustering-Based Model Order Reduction for Nonlinear Network Systems -- 1 Introduction -- 2 Preliminaries -- 2.1 Graph Theory -- 2.2 Graph Partitions -- 2.3 Linear Multi-agent Systems -- 2.4 Clustering-Based Model Order Reduction -- 2.5 Model Reduction for Non-asymptotically Stable Systems -- 3 Clustering for Linear Multi-agent Systems -- 4 Clustering for Nonlinear Multi-agent Systems -- 4.1 Nonlinear Multi-agent Systems -- 4.2 Clustering by Projection -- 5 Numerical Examples -- 5.1 Small Network Example -- 5.2 van der Pol Oscillators -- 6 Conclusions -- References -- Adaptive Interpolatory MOR by Learning the Error Estimator in the Parameter Domain -- 1 Introduction -- 2 Interpolatory MOR -- 3 Greedy Method for Choosing Interpolation Points -- 4 Adaptive Training by Learning the Error Estimator in the Parameter Domain -- 4.1 Radial Basis Functions -- 4.2 Learning the Error Estimator over the Parameter Domain -- 4.3 Adaptive Choice of Interpolation Points with Surrogate Error Estimator -- 5 Numerical Examples -- 5.1 RLC Interconnect Circuit -- 5.2 Thermal Model -- 5.3 Dual-Mode Circular Waveguide Filter -- 6 Conclusion -- References -- A Link Between Gramian-Based Model Order Reduction and Moment Matching -- 1 Introduction -- 1.1 Balancing of LTI Systems -- 1.2 Rational Interpolation -- 1.3 Organization of Paper -- 2 Gramian Quadrature Algorithm -- 2.1 Approximating the Gramian via Runge-Kutta Methods -- 2.2 Computation of mathcalHj in Algorithm 1 -- 2.3 The Space Spanned by the Approximate Cholesky Factor Z -- 3 Approximate Balancing Transformation -- 4 Connection to Other Methods -- 4.1 Balanced POD -- 4.2 The ADI Iteration -- 5 Examples -- 6 Conclusion -- References. ; Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms -- 1 Introduction -- 2 Empirical Gramians for Linear Systems -- 2.1 Empirical Controllability Gramian -- 2.2 Empirical Observability Gramian -- 2.3 Empirical Cross Gramian -- 2.4 Parametric Empirical Gramians -- 3 Empirical-Gramian-Based Model Reduction -- 3.1 Empirical Poor Man -- 3.2 Empirical Approximate Balancing -- 3.3 Empirical Dominant Subspaces -- 3.4 Empirical Balanced Truncation -- 3.5 Empirical Balanced Gains -- 4 Approximate Norms -- 4.1 Signal Norms -- 4.2 System Norms -- 4.3 Modified Induced Norms -- 4.4 Parametric Norms -- 5 MORscore -- 6 Benchmark Comparison -- 6.1 emgr - EMpirical GRamian Framework -- 6.2 Thermal Block Benchmark -- 6.3 Numerical Results -- 7 Conclusion -- References -- Optimization-Based Parametric Model Order Reduction for the Application to the Frequency-Domain Analysis of Complex Systems -- 1 Introduction -- 2 Basics of the Global Basis and Krylov Subspace Method -- 2.1 Krylov Subspaces -- 2.2 Affine Matrix Decomposition -- 3 OGPA: Optimization-based Greedy Parameter Sampling -- 3.1 Grid-Free Sampling -- 3.2 A-Posteriori Model Quality Evaluation -- 4 Numerical Examples -- 4.1 Cantilever Solid Beam -- 4.2 Rear Axle Carrier -- 5 Summary -- References -- On Extended Model Order Reduction for Linear Time Delay Systems -- 1 Introduction -- 2 Problem Statement -- 3 Observability and Controllability Inequalities -- 4 Model order reduction by truncation -- 5 Feasibility of the Matrix Inequalities -- 6 Example: Delay Neural Fields -- 7 Application to Parameterized Model Reduction -- 7.1 Example -- 8 Conclusions -- References -- *-20pt Applications of Model Order Reduction -- A Practical Method for the Reductionpg of Linear Thermo-Mechanical Dynamic Equations -- 1 Introduction -- 2 The Thermo-Mechanical Model -- 2.1 Structural Mechanics. ; 2.2 Heat Transfer -- 2.3 Coupling of Equations -- 3 Derivation of the Reduction Algorithm -- 3.1 Model Order Reduction -- 3.2 Extraction of the Coupling Matrix -- 3.3 Algorithm -- 4 Implementation and Results -- 4.1 Modeling -- 4.2 Results -- 5 Conclusions -- References -- Reduced-Order Methods in Medical Imaging -- 1 Introduction -- 2 Methods -- 2.1 Medical Tomography -- 2.2 Proper Orthogonal Decomposition -- 2.3 Downsampled POD Method -- 2.4 Hybrid-POD Method -- 2.5 Implementation Details -- 3 Results -- 3.1 Test Tube with Fish Eggs -- 3.2 Down-Sampling Results -- 3.3 Hybrid-POD Method -- 4 Discussion -- 5 Conclusion -- References -- Efficient Krylov Subspace Techniques for Model Order Reduction of Automotive Structures in Vibroacoustic Applications -- 1 Introduction -- 2 Krylov-Based Model Order Reduction -- 2.1 Problem Definition -- 2.2 Reduction Framework -- 3 Numerical Implementation -- 4 Results -- 4.1 Generic System -- 4.2 Coupled System -- 5 Conclusions and Remarks -- References -- Model-Based Adaptive MOR Framework for Unsteady Flows Around Lifting Bodies -- 1 Introduction -- 2 Linear Reduced Basis Methods -- 3 Adaptive Approach -- 3.1 Physical Problem: Navier-Stokes Equations -- 3.2 Error Estimation -- 3.3 Sensitivity -- 4 Demonstration on Lifting Surfaces -- 4.1 Stalled NACA0012 Airfoil -- 4.2 High-Lift 30P30N Airfoil -- 5 Final Remarks and Outlook -- References -- Reduced Basis Methods for Quasilinear Elliptic PDEs with Applications to Permanent Magnet Synchronous Motors -- 1 Introduction -- 2 The Quasilinear Parametric Elliptic PDE -- 2.1 Abstract Formulation -- 3 Reduced Basis Approximation -- 3.1 An EIM-RB Method -- 3.2 Error Estimation -- 3.3 Computational Procedure -- 3.4 Numerical Results -- 4 Conclusion -- References -- Structure-Preserving Reduced- Order Modeling of Non-Traditional Shallow Water Equation -- 1 Introduction. ; 2 Shallow Water Equation -- 3 Full- Order Model -- 4 Reduced- Order Model -- 5 Numerical Results -- 5.1 Single-Layer Geostrophic Adjustment -- 5.2 Single-Layer Shear Instability -- 6 Conclusions -- References -- *-20pt Benchmarks and Software of Model Order Reduction -- A Non-stationary Thermal-Block Benchmark Model for Parametric Model Order Reduction -- 1 Introduction -- 2 Problem Description -- 3 Problem Variants -- 3.1 Four-Parameter LTI System -- 3.2 Single-Parameter LTI System -- 3.3 Non-parametric LTI System -- 4 Conclusion -- References -- Parametric Model Order Reduction Using pyMOR -- 1 Introduction -- 2 Software Design -- 3 Overview of Model Order Reduction Methods -- 3.1 Reduced Basis Method -- 3.2 System-Theoretic Methods -- 4 Numerical Results -- 4.1 Non-parametric Version -- 4.2 Single-Parameter Version -- 4.3 Four-Parameter Version -- 5 Conclusions -- References -- Matrix Equations, Sparse Solvers: M-M.E.S.S.-2.0.1-Philosophy, Features, and Application for (Parametric) Model Order Reduction -- 1 Introduction -- 1.1 A Brief History of M-M.E.S.S. -- 1.2 Structure of This Chapter -- 2 M-M.E.S.S.-Philosophy and Features -- 2.1 Available Solver Functions and Underlying Methods -- 3 Model Order Reduction in M-M.E.S.S. -- 3.1 IRKA and Classic Balanced Truncation -- 3.2 Further Variants of Balanced Truncation -- 4 Parametric Model Order Reduction Using M-M.E.S.S. -- 4.1 Piecewise MOR -- 4.2 Interpolation of Transfer Functions -- 5 Numerical Experiments -- References -- MORLAB-The Model Order Reduction LABoratory -- 1 Introduction -- 2 Code Design Principles -- 2.1 Toolbox Structure -- 2.2 Function Interfaces -- 2.3 Documentation -- 3 Additive System Decomposition Approach -- 3.1 Standard System Case -- 3.2 Descriptor System Case -- 4 Model Reduction with the MORLAB Toolbox -- 4.1 First-Order Methods -- 4.2 Second-Order Methods. ; 5 Numerical Examples.
• Titolo autorizzato: Model reduction of complex dynamical systems
• ISBN: 3-030-72983-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466393103316
• Lo trovi qui: Univ. di Salerno
• Serie: International Series of Numerical Mathematics