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Large-Scale Networks in Engineering and Life Sciences / / edited by Peter Benner, Rolf Findeisen, Dietrich Flockerzi, Udo Reichl, Kai Sundmacher
| Large-Scale Networks in Engineering and Life Sciences / / edited by Peter Benner, Rolf Findeisen, Dietrich Flockerzi, Udo Reichl, Kai Sundmacher |
| Edizione | [1st ed. 2014.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2014 |
| Descrizione fisica | 1 online resource (401 p.) |
| Disciplina | 003.71 |
| Collana | Modeling and Simulation in Science, Engineering and Technology |
| Soggetto topico |
Mathematics
Differential equations Mathematics - Data processing Applications of Mathematics Differential Equations Computational Science and Engineering |
| ISBN | 3-319-08437-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- 1 Introduction to the Geometric Theory of ODEs with Applications to Chemical Processes, Dietrich Flockerzi -- 2 Mathematical Modeling and Analysis of Nonlinear Time-Invariant RLC Circuits, Timo Reis -- 3 Interacting with Networks of Mobile Agents, Magnus Egerstedt, Jean-Pierre de la Croix, Hiroaki Kawashima, and Peter Kingston -- 4 Combinatorial optimization: the interplay of graph theory, linear and integer programming illustrated on network flow, Annegret K. Wagler -- 5 Stoichiometric and Constraint-based Analysis of Biochemical Reaction Networks, Steffen Klamt, Oliver Hädicke and Axel von Kamp -- 6 A Petri Net based Framework for Biomodel Engineering, Mary Ann Blätke, Christian Rohr, Monika Heiner and Wolfgang Marwan -- 7 Hybrid Modeling for Systems Biology: Theory and Practice, Moritz von Stosch, Nuno Carinhas and Rui Oliveira. |
| Record Nr. | UNINA-9910299969703321 |
| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Model Order Reduction . Volume 3 Applications / / Peter Benner, Wil Schilders, Stefano Grivet-Talocia, Alfio Quarteroni, Gianluigi Rozza, Luís Miguel Silveira
| Model Order Reduction . Volume 3 Applications / / Peter Benner, Wil Schilders, Stefano Grivet-Talocia, Alfio Quarteroni, Gianluigi Rozza, Luís Miguel Silveira |
| Autore | Benner Peter |
| Pubbl/distr/stampa | Berlin/Boston, : De Gruyter, 2020 |
| Descrizione fisica | 1 online resource (VIII, 466 p.) |
| Disciplina | 515.353 |
| Collana | Model Order Reduction |
| Soggetto topico | MATHEMATICS / Numerical Analysis |
| Soggetto non controllato |
Complexity reduction
applications in engineering biomedical engineering computational physics computer science |
| ISBN |
3-11-049775-1
3-11-049900-2 |
| Classificazione | SK 955 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Preface to the third volume of Model Order Reduction -- Contents -- 1 Model reduction in chemical process optimization -- 2 Model order reduction in mechanical engineering -- 3 Case studies of model order reduction for acoustics and vibrations -- 4 Model order reduction in microelectronics -- 5 Complexity reduction of electromagnetic systems -- 6 Model reduction in computational aerodynamics -- 7 Model order reduction in neuroscience -- 8 Reduced-order modeling for applications to the cardiovascular system -- 9 From the POD-Galerkin method to sparse manifold models -- 10 Model order reduction in uncertainty quantification -- 11 Reduced-order modeling of large-scale network systems -- 12 Model order reduction and digital twins -- 13 MOR software -- Index |
| Record Nr. | UNINA-9910437642603321 |
Benner Peter
|
||
| Berlin/Boston, : De Gruyter, 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Model Order Reduction . Volume 3 Applications / / Peter Benner, Wil Schilders, Stefano Grivet-Talocia, Alfio Quarteroni, Gianluigi Rozza, Luís Miguel Silveira
| Model Order Reduction . Volume 3 Applications / / Peter Benner, Wil Schilders, Stefano Grivet-Talocia, Alfio Quarteroni, Gianluigi Rozza, Luís Miguel Silveira |
| Autore | Benner Peter |
| Pubbl/distr/stampa | Berlin/Boston, : De Gruyter, 2020 |
| Descrizione fisica | 1 online resource (VIII, 466 p.) |
| Disciplina | 515.353 |
| Collana | Model Order Reduction |
| Soggetto topico | MATHEMATICS / Numerical Analysis |
| Soggetto non controllato |
Complexity reduction
applications in engineering biomedical engineering computational physics computer science |
| ISBN |
3-11-049775-1
3-11-049900-2 |
| Classificazione | SK 955 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Preface to the third volume of Model Order Reduction -- Contents -- 1 Model reduction in chemical process optimization -- 2 Model order reduction in mechanical engineering -- 3 Case studies of model order reduction for acoustics and vibrations -- 4 Model order reduction in microelectronics -- 5 Complexity reduction of electromagnetic systems -- 6 Model reduction in computational aerodynamics -- 7 Model order reduction in neuroscience -- 8 Reduced-order modeling for applications to the cardiovascular system -- 9 From the POD-Galerkin method to sparse manifold models -- 10 Model order reduction in uncertainty quantification -- 11 Reduced-order modeling of large-scale network systems -- 12 Model order reduction and digital twins -- 13 MOR software -- Index |
| Record Nr. | UNISA-996398645103316 |
|
Benner Peter
|
||
| Berlin/Boston, : De Gruyter, 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Model Order Reduction . Volume 2 Snapshot-Based Methods and Algorithms / / Peter Benner, Wil Schilders, Stefano Grivet-Talocia, Alfio Quarteroni, Gianluigi Rozza, Luís Miguel Silveira
| Model Order Reduction . Volume 2 Snapshot-Based Methods and Algorithms / / Peter Benner, Wil Schilders, Stefano Grivet-Talocia, Alfio Quarteroni, Gianluigi Rozza, Luís Miguel Silveira |
| Autore | Benner Peter |
| Pubbl/distr/stampa | Berlin/Boston, : De Gruyter, 2020 |
| Descrizione fisica | 1 online resource (VIII, 348 p.) |
| Disciplina | 515.353 |
| Collana | Model Order Reduction |
| Soggetto topico | MATHEMATICS / Numerical Analysis |
| Soggetto non controllato |
Applied mathematics
PROM |
| ISBN | 3-11-067149-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Preface to the second volume of Model Order Reduction -- Contents -- 1 Basic ideas and tools for projection-based model reduction of parametric partial differential equations -- 2 Model order reduction by proper orthogonal decomposition -- 3 Proper generalized decomposition -- 4 Reduced basis methods -- 5 Computational bottlenecks for PROMs: precomputation and hyperreduction -- 6 Localized model reduction for parameterized problems -- 7 Data-driven methods for reduced-order modeling -- Index |
| Record Nr. | UNISA-996398645003316 |
|
Benner Peter
|
||
| Berlin/Boston, : De Gruyter, 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Model Order Reduction . Volume 1 System- and Data-Driven Methods and Algorithms / / ed. by Peter Benner
| Model Order Reduction . Volume 1 System- and Data-Driven Methods and Algorithms / / ed. by Peter Benner |
| Pubbl/distr/stampa | Berlin ; ; Boston : , : De Gruyter, , [2021] |
| Descrizione fisica | 1 online resource (X, 378 p.) |
| Disciplina | 515.353 |
| Collana | Model Order Reduction |
| Soggetto topico | MATHEMATICS / Numerical Analysis |
| ISBN | 3-11-049896-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Preface to the first volume of Model Order Reduction -- Contents -- 1 Model order reduction: basic concepts and notation -- 2 Balancing-related model reduction methods -- 3 Model order reduction based on moment-matching -- 4 Modal methods for reduced order modeling -- 5 Post-processing methods for passivity enforcement -- 6 The Loewner framework for system identification and reduction -- 7 Manifold interpolation -- 8 Vector fitting -- 9 Kernel methods for surrogate modeling -- 10 Kriging: methods and applications -- Index |
| Record Nr. | UNISA-996445849203316 |
| Berlin ; ; Boston : , : De Gruyter, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Model Order Reduction . Volume 2 Snapshot-Based Methods and Algorithms / / Peter Benner, Wil Schilders, Stefano Grivet-Talocia, Alfio Quarteroni, Gianluigi Rozza, Luís Miguel Silveira
| Model Order Reduction . Volume 2 Snapshot-Based Methods and Algorithms / / Peter Benner, Wil Schilders, Stefano Grivet-Talocia, Alfio Quarteroni, Gianluigi Rozza, Luís Miguel Silveira |
| Pubbl/distr/stampa | Berlin ; ; Boston : , : De Gruyter, , [2020] |
| Descrizione fisica | 1 online resource (VIII, 348 p.) |
| Disciplina | 515.353 |
| Collana | Model Order Reduction |
| Soggetto topico | MATHEMATICS / Numerical Analysis |
| ISBN | 3-11-067149-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Preface to the second volume of Model Order Reduction -- Contents -- 1 Basic ideas and tools for projection-based model reduction of parametric partial differential equations -- 2 Model order reduction by proper orthogonal decomposition -- 3 Proper generalized decomposition -- 4 Reduced basis methods -- 5 Computational bottlenecks for PROMs: precomputation and hyperreduction -- 6 Localized model reduction for parameterized problems -- 7 Data-driven methods for reduced-order modeling -- Index |
| Record Nr. | UNINA-9910437642503321 |
| Berlin ; ; Boston : , : De Gruyter, , [2020] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Model reduction of complex dynamical systems / / Peter Benner [and five others]
| Model reduction of complex dynamical systems / / Peter Benner [and five others] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer International Publishing, , [2021] |
| Descrizione fisica | 1 online resource (416 pages) |
| Disciplina | 309.173092 |
| Collana | International Series of Numerical Mathematics |
| Soggetto topico |
System theory - History
Dynamics - Statistical methods Teoria de sistemes Dinàmica |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-72983-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNISA-996466393103316 |
| Cham, Switzerland : , : Springer International Publishing, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Model reduction of complex dynamical systems / / Peter Benner [and five others]
| Model reduction of complex dynamical systems / / Peter Benner [and five others] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer International Publishing, , [2021] |
| Descrizione fisica | 1 online resource (416 pages) |
| Disciplina | 309.173092 |
| Collana | International Series of Numerical Mathematics |
| Soggetto topico |
System theory - History
Dynamics - Statistical methods Teoria de sistemes Dinàmica |
| Soggetto genere / forma |
Congressos
Llibres electrònics |
| ISBN | 3-030-72983-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNINA-9910495220303321 |
| Cham, Switzerland : , : Springer International Publishing, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Model Reduction of Parametrized Systems / / edited by Peter Benner, Mario Ohlberger, Anthony Patera, Gianluigi Rozza, Karsten Urban
| Model Reduction of Parametrized Systems / / edited by Peter Benner, Mario Ohlberger, Anthony Patera, Gianluigi Rozza, Karsten Urban |
| Edizione | [1st ed. 2017.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
| Descrizione fisica | 1 online resource (XII, 504 p.) |
| Disciplina | 518 |
| Collana | MS&A, Modeling, Simulation and Applications |
| Soggetto topico |
Computer mathematics
Numerical analysis Applied mathematics Engineering mathematics Mechanics Mechanics, Applied Partial differential equations Computational Mathematics and Numerical Analysis Numeric Computing Mathematical and Computational Engineering Solid Mechanics Partial Differential Equations |
| ISBN | 3-319-58786-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Two ways to treat time in Reduced Basis Methods -- 2 Simultaneous empirical interpolation and reduced basis method. Application to non-linear multi-physics problem -- 3 A Certified Reduced Basis Approach for Parametrized Optimal Control Problems with Two-sided Control Constraints -- 4 A reduced basis method with an exact solution certificate and spatio-parameter adaptivity: application to linear elasticity -- 5 A Reduced Basis Method for Parameter Functions using Wavelet Approximations -- 6 Reduced basis isogeometric mortar approximations for eigenvalue problems in vibroacoustics -- 7 Reduced Basis Approximations for Maxwell’s Equations in Dispersive Media -- 8 Offline Error Bounds for the Reduced Basis Method -- 9 ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics -- 10 Reduced-order semi-implicit schemes for fluid-structure interaction problems -- 11 True Error Control for the Localized Reduced Basis Method for Parabolic Problems -- 12 Automatic reduction of PDEs defined on domains with variable shape -- 13 Localized Reduced Basis Approximation of a Nonlinear Finite Volume Battery Model with Resolved Electrode Geometry -- 14 A-posteriori error estimation of discrete POD models for PDE-constrained optimal control -- 15 Hi-POD solution of parametrized fluid dynamics problems: preliminary results -- 16 Adaptive sampling for nonlinear dimensionality reduction based on manifold learning -- 17 Cross-Gramian-Based Model Reduction: A Comparison -- 18 Truncated Gramians for Bilinear Systems and their Advantages in Model Order Reduction -- 19 Leveraging Sparsity and Compressive Sensing for Reduced Order Modeling -- 20 A HJB-POD approach to the control of the level set equation -- 21 Model order reduction approaches for infinite horizon optimal control problems via the HJB equation -- 22 Interpolatory methods for H model reduction of multi-input/multi-output systems -- 23 Model reduction of linear time-varying systems with applications for moving loads -- 24 Interpolation Strategy for BT-based Parametric MOR of Gas Pipeline-Networks -- 25 Energy stable model order reduction for the Allen-Cahn equation -- 26 MOR-based Uncertainty Quantification in Transcranial Magnetic Stimulation -- 27 Model Order Reduction of Nonlinear Eddy Current Problems using Missing Point Estimation -- 28 On Efficient Approaches for Solving a Cake Filtration Model under Parameter Variation -- 29 Model reduction for coupled near-well and reservoir models using multiple space-time discretizations -- 30 Time-dependent Parametric Model Order Reduction for Material Removal Simulations . |
| Record Nr. | UNINA-9910254310203321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory : Festschrift in Honor of Volker Mehrmann / / edited by Peter Benner, Matthias Bollhöfer, Daniel Kressner, Christian Mehl, Tatjana Stykel
| Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory : Festschrift in Honor of Volker Mehrmann / / edited by Peter Benner, Matthias Bollhöfer, Daniel Kressner, Christian Mehl, Tatjana Stykel |
| Edizione | [1st ed. 2015.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
| Descrizione fisica | 1 online resource (635 p.) |
| Disciplina |
004
510 512.5 515.352 518 519 |
| Soggetto topico |
Numerical analysis
Computer mathematics Matrix theory Algebra Differential equations System theory Numerical Analysis Computational Science and Engineering Linear and Multilinear Algebras, Matrix Theory Ordinary Differential Equations Systems Theory, Control |
| ISBN | 3-319-15260-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | A. Numerical Algebra -- B. Matrix Theory -- C. Differential-Algebraic-Equations and Control Theory -- D. Miscellanea. |
| Record Nr. | UNINA-9910299768703321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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