LEADER 11006nam 2200589 450 001 996466393103316 005 20231110225150.0 010 $a3-030-72983-4 035 $a(CKB)4100000012009056 035 $a(MiAaPQ)EBC6712971 035 $a(Au-PeEL)EBL6712971 035 $a(OCoLC)1265465325 035 $a(PPN)257350977 035 $a(EXLCZ)994100000012009056 100 $a20220605d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aModel reduction of complex dynamical systems /$fPeter Benner [and five others] 210 1$aCham, Switzerland :$cSpringer International Publishing,$d[2021] 210 4$d©2021 215 $a1 online resource (416 pages) 225 1 $aInternational Series of Numerical Mathematics ;$vv.171 311 $a3-030-72982-6 327 $aIntro -- 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. 327 $a5 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. 327 $aComparing (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. 327 $a2.2 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. 327 $a2 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. 327 $a5 Numerical Examples. 410 0$aInternational Series of Numerical Mathematics 606 $aSystem theory$xHistory 606 $aDynamics$xStatistical methods 606 $aTeoria de sistemes$2thub 606 $aDinàmica$2thub 608 $aCongressos$2thub 608 $aLlibres electrònics$2thub 615 0$aSystem theory$xHistory. 615 0$aDynamics$xStatistical methods. 615 7$aTeoria de sistemes 615 7$aDinàmica 676 $a309.173092 702 $aBenner$b Peter 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466393103316 996 $aModel reduction of complex dynamical systems$92860604 997 $aUNISA LEADER 04677nam 2200589Ia 450 001 9910830948603321 005 20230829003132.0 010 $a1-280-72360-2 010 $a9786610723607 010 $a3-527-60817-6 010 $a3-527-60829-X 035 $a(CKB)1000000000377389 035 $a(EBL)482317 035 $a(OCoLC)609855581 035 $a(SSID)ssj0000302755 035 $a(PQKBManifestationID)11947569 035 $a(PQKBTitleCode)TC0000302755 035 $a(PQKBWorkID)10274704 035 $a(PQKB)11271799 035 $a(MiAaPQ)EBC482317 035 $a(EXLCZ)991000000000377389 100 $a20040206d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe mathematics of geometrical and physical optics$b[electronic resource] $ethe k-function and its ramifications /$fOrestes N. Stavroudis 210 $aWeinheim $cWiley-VCH$dc2006 215 $a1 online resource (242 p.) 300 $aDescription based upon print version of record. 311 $a3-527-40448-1 320 $aIncludes bibliographical references and index. 327 $aThe Mathematics of Geometrical and Physical Optics; Acknowledgements; Introduction; Contents; Part I Preliminaries; 1 Fermat's Principle and the Variational Calculus; 1.1 Rays in Inhomogeneous Media; 1.2 The Calculus of Variations; 1.3 The Parametric Representation; 1.4 The Vector Notation; 1.5 The Inhomogeneous Optical Medium; 1.6 The Maxwell Fish Eye; 1.7 The Homogeneous Medium; 1.8 Anisotropic Media; 2 Space Curves and Ray Paths; 2.1 Space Curves; 2.2 The Vector Trihedron; 2.3 The Frenet-Serret Equations; 2.4 When the Parameter is Arbitrary; 2.5 The Directional Derivative 327 $a2.6 The Cylindrical Helix2.7 The Conic Section; 2.8 The Ray Equation; 2.9 More on the Fish Eye; 3 The Hilbert Integral and the Hamilton-Jacobi Theory; 3.1 A Digression on the Gradient; 3.2 The Hilbert Integral. Parametric Case; 3.3 Application to Geometrical Optics; 3.4 The Condition for Transversality; 3.5 The Total Differential Equation; 3.6 More on the Helix; 3.7 Snell's Law; 3.8 The Hamilton-Jacobi Partial Differential Equations; 3.9 The Eikonal Equation; 4 The Differential Geometry of Surfaces.; 4.1 Parametric Curves; 4.2 Surface Normals; 4.3 The Theorem of Meusnier 327 $a5.7 The Eikonal Equation. The Complete Integral5.8 The Eikonal Equation. The General Solution; 5.9 The Eikonal Equation. Proof of the Pudding; Part II The k-function; 6 The Geometry of Wave Fronts; 6.1 Preliminary Calculations; 6.2 The Caustic Surface; 6.3 Special Surfaces I: Plane and Spherical Wavefronts; 6.4 Parameter Transformations; 6.5 Asymptotic Curves and Isotropic Directions; 7 Ray Tracing: Generalized and Otherwise; 7.1 The Transfer Equations; 7.2 The Ancillary Quantities; 7.3 The Refraction Equations; 7.4 Rotational Symmetry; 7.5 The Paraxial Approximation 327 $a7.6 Generalized Ray Tracing - Transfer7.7 Generalized Ray Tracing - Preliminary Calculations; 7.8 Generalized Ray Tracing - Refraction; 7.9 The Caustic; 7.10 The Prolate Spheroid; 7.11 Rays in the Spheroid; 8 Aberrations in Finite Terms; 8.1 Herzberger's Diapoints; 8.2 Herzberger's Fundamental Optical Invariant; 8.3 The Lens Equation; 8.4 Aberrations in Finite Terms; 8.5 Half-Symmetric, Symmetric and Sharp Images; 9 Refracting the k-Function; 9.1 Refraction; 9.2 The Refracting Surface; 9.3 The Partial Derivatives; 9.4 The Finite Object Point; 9.5 The Quest for C; 9.6 Developing the Solution 327 $a9.7 Conclusions 330 $aIn this sequel to his book, ""The Optics of Rays, Wavefronts, and Caustics,"" Stavroudis not only covers his own research results, but also includes more recent developments. The book is divided into three parts, starting with basic mathematical concepts that are further applied in the book. Surface geometry is treated with classical mathematics, while the second part covers the k-function, discussing and solving the eikonal equation as well as Maxwell equations in this context. A final part on applications consists of conclusions drawn or developed in the first two parts of the book, discussi 606 $aGeometrical optics$xMathematics 606 $aPhysical optics$xMathematics 615 0$aGeometrical optics$xMathematics. 615 0$aPhysical optics$xMathematics. 676 $a535.32 700 $aStavroudis$b O. 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