Novel Mathematics Inspired by Industrial Challenges (Mathematics in Industry, 38)

Description

This contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics. The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields. 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