Novel mathematics inspired by industrial challenges / / edited by Michael Günther, Wil Schilders

• Record Nr.: UNINA9910558497203321
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 3-030-96173-7
• Descrizione fisica: 1 online resource (348 pages)
• Collana: Mathematics in Industry ; ; v.38
• Disciplina: 620.00151
• Soggetti: Industrial engineering - Mathematics; Enginyeria industrial; Matemàtica; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Acknowledgements -- Contents -- List of Contributors -- Part I Computational Science and Engineering -- Multirate Schemes - An Answer of Numerical Analysis to a Demand from Applications -- 1 Introduction -- 2 Strategies for multirate and convergence -- 2.1 Combining extra- and interpolation for multirate properly -- 2.2 Linear multistep methods -- 2.3 Runge-Kutta schemes -- 2.4 Overview on multirate strategies -- 3 Dynamic iteration and multiphysics -- 4 Applications in circuit simulation -- 4.1 Partitioned network modeling -- 4.2 Multirate schemes -- 4.3 Thermal-electric coupling-silicon on insulator -- 5 Molecular dynamics -- 6 Conclusion and outlook -- References -- Electronic Circuit Simulation and the Development of New Krylov-Subspace Methods -- 1 Introduction -- 1.1 The Central Numerical Task in Circuit Simulation -- 1.2 Large-Scale Matrix Computations and Krylov-Subspace Methods -- 1.3 The Special Case of Circuit Interconnect Analysis -- 1.4 Outline -- 2 From AWE to the PVL Algorithm -- 2.1 Elmore Delay and AWE -- 2.2 PVL Algorithm -- 2.3 An Example -- 3 Krylov Subspaces with Multiple Starting Vectors -- 3.1 Block Krylov Subspaces -- 3.2 Block Lanczos Method -- 4 A New Approch: the Band Lanczos Method -- 4.1 Defining Properties -- 4.2 ; Reduced-Order Models and Matrix Padé Approximants -- 4.3 An Actual Algorithm -- 5 Structure Preservation -- 6 Band Arnoldi Process -- 7 Concluding Remarks -- References -- Modular time integration of coupled problems in system dynamics -- 1 Introduction -- 2 Model based simulation of pantograph-catenary interaction -- Catenary first -- Pantograph first -- Engineering application -- Mathematical aspects of modular simulation -- 3 Modular time integration: The ODE case -- 4 Modular time integration: The DAE case -- Preconditioning -- Related work -- References.; Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems -- 1 Introduction -- 2 Differential-algebraic equations -- 2.1 How the topic of DAEs emerged -- 2.2 Electrical circuits -- 2.3 Constrained mechanical systems -- 3 Major results and numerical methods -- 3.1 Perturbation index and implicit Runge-Kutta methods -- 3.2 DAEs and differential geometry -- 3.3 Singularly perturbed problems and regularization -- 3.4 General fully implicit DAEs -- 3.5 Constrained Hamiltonian systems -- 4 Beyond classical DAEs -- 4.1 Navier-Stokes incompressible -- 4.2 Stochastic DAEs -- 5 Nonsmooth dynamical systems -- 5.1 A short zoology -- 5.1.1 Unilateral constraints and Moreau's sweeping process -- 5.1.2 Projected dynamical systems -- 5.1.3 Variational inequalities -- 5.1.4 Complementarity dynamic systems -- 5.1.5 Differential variational inequalities -- 5.1.6 Derivatives of functions of bounded variation -- 5.1.7 Measure differential equations and measure differential inclusions -- 5.1.8 A very diverse field -- 5.2 Nonsmooth mechanical systems with impacts -- 5.2.1 Hamilton's principle as a differential inclusion -- 5.2.2 Forces and Accelerations are Measures -- 5.2.3 Existence of Lagrangian multipliers -- 5.3 Numerical solution strategies -- 5.3.1 Event-driven and event-capturing methods -- 5.3.2 Nonsmooth time-stepping -- 5.3.3 Dealing with collisions -- 5.3.4 Dealing with complementarity -- 5.3.5 Augmented Lagrangian and projected Gauß-Seidel -- 5.3.6 Recent developments -- Summary -- Acknowledgments -- References -- Fast Numerical Methods to Compute Periodic Solutions of Electromagnetic Models -- 1 Starting Point in Electrical Engineering -- 1.1 Methodology Motivation from a Toy Model -- 2 Statement of the Problem. Mathematical Modelling -- 3 Existing Mathematics.; 4 A Novel and Efficient Methodology to Solve the Problem -- 4.1 Reduced Problem -- 4.2 Approximating the Initial Currents in Rotor Bars -- 4.3 Numerical Results -- 5 Current State of Art -- 6 Conclusions -- References -- Challenges in the Simulation of Radio Frequency Circuits -- 1 Introduction -- 2 Network equations -- 3 Simulation of Radio Frequency Circuits -- 4 The Embedding Technique -- References -- An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics -- 1 Introduction -- 2 From digital twin to real-time analysis -- 3 Advanced geometrical parametrization with automatic CAD files interface -- 4 Parameter space dimensionality reduction -- 5 Data driven model order reduction -- 5.1 Dynamic mode decomposition -- 5.2 Proper orthogonal decomposition with interpolation -- 6 Simulation-based design optimization framework -- 7 Conclusions and perspectives -- Acknowledgment -- Competing Interests -- Ethics approval and consent to participate -- Availability of data and materials -- Funding acknowledgements -- References -- From rotating fluid masses and Ziegler's paradox to Pontryagin- and Krein spaces and bifurcation theory -- 1 Historical background -- 1.1 Stability of Kelvin's gyrostat and spinning artillery shells filled with liquid -- 1.2 Secular instability of the Maclaurin spheroids by viscous and radiative losses -- 1.3 ; Brouwer's rotating vessel -- Stability and instability without friction -- Stability of triangular libration points L4 and L5 -- Destabilization by friction -- Indefinite damping and PT-symmetry -- 2 Ziegler's paradox -- 3 Bottema's analysis of Ziegler's paradox -- 4 An umbrella without dynamics -- 5 Hopf bifurcation near 1:1 resonance and structural stability -- 6 Abscissa minimization, robust stability and heavy damping -- Abscissa minimization and multiple roots.; Swallowtail singularity as the global minimizer of the abscissa -- References -- Part II Data Analysis and finance -- Topological Data Analysis -- 1 Introduction -- About this paper -- 2 The need of new mathematical and algorithmic tools -- 3 The emergence of geometric inference and persistent homology -- 3.1 Distance-based geometric inference -- Covers and nerves to compute the topology of union of balls -- Another use of covers and nerves: the Mapper algorithm -- Distance-based inference with noisy data -- 3.2 Persistent homology -- Persistent homology for machine learning -- The algorithmic and software challenges of TDA -- 4 New research directions -- 5 Conclusion -- A brief glossary -- References -- Prediction Models with Functional Data for Variables related with Energy Production -- 1 Introduction -- 2 Functional Data Models -- 2.1 Application to Iberian Market Energy -- 3 Variable selection -- 3.1 The selection algorithm -- 3.2 Numerical results -- 4 Real data application -- 4.1 Energy Market Demand -- 4.2 Energy Price -- 5 Conclusions -- References -- Quantization Methods for Stochastic Differential Equations -- 1 Introduction -- 1.1 Finance and Stochastic Differential Equations -- 1.2 Quantization -- 1.3 Outline of the Paper -- 2 Vector Quantization -- 2.1 Optimal Quantization Grids -- 2.2 Numerical Methods -- 2.2.1 Lloyd's Algorithm -- 2.2.2 The Newton-Raphson Algorithm -- 3 Recursive Marginal Quantization -- 3.1 Numerical Methods -- 3.2 The Zero Boundary -- 3.3 Higher-order Updates -- 4 Recursive Marginal Quantization for Stochastic Volatility Models -- 5 Numerical Results -- 5.1 Numerical Convergence Results -- 5.2 An Example of a Local Volatility Model -- 5.3 Stochastic Volatility Models -- 5.4 Calibration -- 6 Conclusion -- References -- Index.