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Model Order Reduction and Applications [[electronic resource] ] : Cetraro, Italy 2021 / / by Michael Hinze, J. Nathan Kutz, Olga Mula, Karsten Urban ; edited by Maurizio Falcone, Gianluigi Rozza
| Model Order Reduction and Applications [[electronic resource] ] : Cetraro, Italy 2021 / / by Michael Hinze, J. Nathan Kutz, Olga Mula, Karsten Urban ; edited by Maurizio Falcone, Gianluigi Rozza |
| Autore | Hinze Michael |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (241 pages) |
| Disciplina | 518 |
| Altri autori (Persone) |
KutzJ. Nathan
MulaOlga UrbanKarsten FalconeMaurizio RozzaGianluigi |
| Collana | C.I.M.E. Foundation Subseries |
| Soggetto topico |
Numerical analysis
Mathematical models Mathematics—Data processing Differential equations Numerical Analysis Mathematical Modeling and Industrial Mathematics Computational Mathematics and Numerical Analysis Differential Equations Equacions diferencials Models matemàtics |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-29563-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996538660903316 |
Hinze Michael
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| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Model Order Reduction and Applications : Cetraro, Italy 2021 / / by Michael Hinze, J. Nathan Kutz, Olga Mula, Karsten Urban ; edited by Maurizio Falcone, Gianluigi Rozza
| Model Order Reduction and Applications : Cetraro, Italy 2021 / / by Michael Hinze, J. Nathan Kutz, Olga Mula, Karsten Urban ; edited by Maurizio Falcone, Gianluigi Rozza |
| Autore | Hinze Michael |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (241 pages) |
| Disciplina | 518 |
| Altri autori (Persone) |
KutzJ. Nathan
MulaOlga UrbanKarsten FalconeMaurizio RozzaGianluigi |
| Collana | C.I.M.E. Foundation Subseries |
| Soggetto topico |
Numerical analysis
Mathematical models Mathematics—Data processing Differential equations Numerical Analysis Mathematical Modeling and Industrial Mathematics Computational Mathematics and Numerical Analysis Differential Equations Equacions diferencials Models matemàtics |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-29563-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910731466603321 |
|
Hinze Michael
|
||
| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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 | ||
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Partial differential equations : an introduction to analytical and numerical methods / / Wolfgang Arendt, Karsten Urban ; translated by James B. Kennedy
| Partial differential equations : an introduction to analytical and numerical methods / / Wolfgang Arendt, Karsten Urban ; translated by James B. Kennedy |
| Autore | Arendt Wolfgang <1950-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2023] |
| Descrizione fisica | 1 online resource (463 pages) |
| Disciplina | 515.353 |
| Collana | Graduate texts in mathematics |
| Soggetto topico | Differential equations, Partial |
| ISBN | 3-031-13379-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Foreword by the Translator -- Preface -- Acknowledgments -- About the Authors -- About the Translator -- Contents -- List of figures -- 1 Modeling, or where do differential equations come from -- 1.1 Mathematical modeling -- 1.1.1 Modeling with partial differential equations -- 1.1.2 Modeling is only the first step -- 1.2 Transport processes -- 1.2.1 Conservation laws -- 1.2.2 From a conservation law to a differential equation -- 1.2.3 The linear transport equation -- 1.2.4 The convection-reaction equation -- 1.2.5* Burgers' equation -- 1.3 Diffusion -- 1.4 The wave equation -- 1.5 The Black-Scholes equation -- 1.6 Let's get higher dimensional -- 1.6.1 Transport processes -- 1.6.2 Diffusion processes -- 1.6.3 The wave equation -- 1.6.4 Laplace's equation -- 1.7* But there's more -- 1.7.1 The KdV equation -- 1.7.2 Geometric differential equations -- 1.7.3 The plate equation -- 1.7.4 The Navier-Stokes equations -- 1.7.5 Maxwell's equations -- 1.7.6 The Schrödinger equation -- 1.8 Classification of partial differential equations -- 1.9* Comments -- 1.10 Exercises -- 2 Classification and characteristics -- 2.1 Characteristics of initial value problems on ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R) /StPNE pdfmark [/StBMC pdfmarkRps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 2.1.1 Homogeneous problems -- 2.1.2 Inhomogeneous problems -- 2.1.3* Burgers' equation -- 2.2 Equations of second order -- 2.3* Nonlinear equations of second order -- 2.4* Equations of higher order and systems -- 2.5 Exercises -- 3 Elementary methods -- 3.1 The one-dimensional wave equation -- 3.1.1 D'Alembert's formula on ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R times double struck upper R) /StPNE pdfmark [/StBMC pdfmarkR Rps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark.
3.1.2 The wave equation on an interval -- 3.2 Fourier series -- 3.3 Laplace's equation -- 3.3.1 The Dirichlet problem on the unit square -- 3.3.2 The Dirichlet problem on the disk -- 3.3.3 The elliptic maximum principle -- 3.3.4 Well-posedness of the Dirichlet problem for the square and the disk -- 3.4 The heat equation -- 3.4.1 Separation of variables -- 3.4.2 The parabolic maximum principle -- 3.4.3 Well-posedness of the parabolic initial-boundary value problem on the interval -- 3.4.4 The heat equation in ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R Superscript d) /StPNE pdfmark [/StBMC pdfmarkRdps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 3.5 The Black-Scholes equation -- 3.6 Integral transforms -- 3.6.1 The Fourier transform -- 3.6.2* The Laplace transform -- 3.7 Outlook -- 3.8 Exercises -- 4 Hilbert spaces -- 4.1 Inner product spaces -- 4.2 Orthonormal bases -- 4.3 Completeness -- 4.4 Orthogonal projections -- 4.5 Linear and bilinear forms -- 4.5.1* Extensions and generalizations -- 4.6 Weak convergence -- 4.7 Continuous and compact operators -- 4.8 The spectral theorem -- 4.9* Comments on Chapter 4 -- 4.10 Exercises -- 5 Sobolev spaces and boundary value problems in dimension one -- 5.1 Sobolev spaces in one variable -- 5.2 Boundary value problems on the interval -- 5.2.1 Dirichlet boundary conditions -- 5.2.2 Neumann boundary conditions -- 5.2.3 Robin boundary conditions -- 5.2.4 Mixed and periodic boundary conditions -- 5.2.5 Non-symmetric differential operators -- 5.2.6* A variational approach to singularly perturbed problems and the transport equation -- 5.3* Comments on Chapter 5 -- 5.4 Exercises -- 6 Hilbert space methods for elliptic equations -- 6.1 Mollifiers -- 6.2 Sobolev spaces on ΩRd -- 6.3 The space H10 (Ω) -- 6.4 Lattice operations on H1(Ω). 6.5 The Poisson equation with Dirichlet boundary conditions -- 6.6 Sobolev spaces and Fourier transforms -- 6.7 Local regularity -- 6.8 Inhomogeneous Dirichlet boundary conditions -- 6.9 The Dirichlet problem -- 6.10 Elliptic equations with Dirichlet boundary conditions -- 6.11 H2-regularity -- 6.12* Comments on Chapter 6 -- 6.13 Exercises -- 7 Neumann and Robin boundary conditions -- 7.1 Gauss's theorem -- 7.2 Proof of Gauss's theorem -- 7.3 The extension property -- 7.4 The Poisson equation with Neumann boundary conditions -- 7.5 The trace theorem and Robin boundary conditions -- 7.6* Comments on Chapter 7 -- 7.7 Exercises -- 8 Spectral decomposition and evolution equations -- 8.1 A vector-valued initial value problem -- 8.2 The heat equation: Dirichlet boundary conditions -- 8.3 The heat equation: Robin boundary conditions -- 8.4 The wave equation -- 8.5 Inhomogeneous parabolic equations -- 8.6* Space/time variational formulations -- 8.7* Comments on Chapter 8 -- 8.8 Exercises -- 9 Numerical methods -- 9.1 Finite differences for elliptic problems -- 9.1.1 FDM: the one-dimensional case -- 9.1.2 FDM: the two-dimensional case -- 9.2 Finite elements for elliptic problems -- 9.2.1 The Galerkin method -- 9.2.2 Triangulation and approximation on triangles -- 9.2.3 Affine functions on triangles -- 9.2.4 Norms on triangles -- 9.2.5 Transformation into a reference element -- 9.2.6 Interpolation for finite elements -- 9.2.7 Finite element spaces -- 9.2.8 The Poisson problem on polygons -- 9.2.9 The stiffness matrix and the linear system of equations -- 9.2.10 Numerical experiments -- 9.3* Extensions and generalizations -- 9.3.1 The Petrov-Galerkin method -- 9.3.2 Further extensions -- 9.4 Parabolic problems -- 9.4.1 Finite differences -- 9.4.2 Finite elements -- 9.4.3* Error estimates via space/time variational formulations -- 9.5 The wave equation. 9.5.1 Finite differences -- 9.5.2 Finite elements -- 9.6* Comments on Chapter 9 -- 9.7 Exercises -- 10 Maple®, or why computers can sometimes help -- 10.1 Maple® -- 10.1.1 Elementary examples -- 10.1.2 Solutions via Fourier transforms -- 10.1.3 Laplace transforms -- 10.1.4 It can also be done numerically -- 10.1.5 Calculating function values -- 10.2 Exercises -- Appendix -- A.1 Banach spaces and linear operators -- A.2 The space C(K) -- A.3 Integration -- A.4 More details on the Black-Scholes equation -- A.4.1 Basics of stochastics -- A.4.2 Black-Scholes model -- A.4.3 The fair price -- References -- Index of names -- Index of symbols -- Index. |
| Record Nr. | UNINA-9910637713003321 |
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Arendt Wolfgang <1950->
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| Cham, Switzerland : , : Springer, , [2023] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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