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Gunther M.Novel Mathematics Inspired by Industrial Challeng.2022
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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
List of Contributors
Computational Science and Engineering
Multirate Schemes — An Answer of Numerical Analysis to a Demand from Applications
Introduction
Strategies for multirate and convergence
Combining extra- and interpolation for multirate properly
Linear multistep methods
Runge-Kutta schemes
Overview on multirate strategies
Dynamic iteration and multiphysics
Applications in circuit simulation
Partitioned network modeling
Multirate schemes
Thermal-electric coupling—silicon on insulator
Molecular dynamics
Conclusion and outlook
References
Electronic Circuit Simulation and the Development of New Krylov-Subspace Methods
Introduction
The Central Numerical Task in Circuit Simulation
Large-Scale Matrix Computations and Krylov-Subspace Methods
The Special Case of Circuit Interconnect Analysis
Outline
From AWE to the PVL Algorithm
Elmore Delay and AWE
PVL Algorithm
An Example
Krylov Subspaces with Multiple Starting Vectors
Block Krylov Subspaces
Block Lanczos Method
A New Approch: the Band Lanczos Method
Defining Properties
Reduced-Order Models and Matrix Padé Approximants
An Actual Algorithm
Structure Preservation
Band Arnoldi Process
Concluding Remarks
References
Modular time integration of coupled problems in system dynamics
Introduction
Model based simulation of pantograph-catenary interaction
Catenary first
Pantograph first
Engineering application
Mathematical aspects of modular simulation
Modular time integration: The ODE case
Modular time integration: The DAE case
Preconditioning
Related work
References
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
Introduction
Differential-algebraic equations
How the topic of DAEs emerged
Electrical circuits
Constrained mechanical systems
Major results and numerical methods
Perturbation index and implicit Runge-Kutta methods
DAEs and differential geometry
Singularly perturbed problems and regularization
General fully implicit DAEs
Constrained Hamiltonian systems
Beyond classical DAEs
Navier-Stokes incompressible
Stochastic DAEs
Nonsmooth dynamical systems
A short zoology
Unilateral constraints and Moreau’s sweeping process
Projected dynamical systems
Variational inequalities
Complementarity dynamic systems
Differential variational inequalities
Derivatives of functions of bounded variation
Measure differential equations and measure differential inclusions
A very diverse field
Nonsmooth mechanical systems with impacts
Hamilton’s principle as a differential inclusion
Forces and Accelerations are Measures
Existence of Lagrangian multipliers
Numerical solution strategies
Event–driven and event–capturing methods
Nonsmooth time–stepping
Dealing with collisions
Dealing with complementarity
Augmented Lagrangian and projected Gauß–Seidel
Recent developments
Summary
Acknowledgments
References
Fast Numerical Methods to Compute Periodic Solutions of Electromagnetic Models
Starting Point in Electrical Engineering
Methodology Motivation from a Toy Model
Statement of the Problem Mathematical Modelling
Existing Mathematics
A Novel and Efficient Methodology to Solve the Problem
Reduced Problem
Approximating the Initial Currents in Rotor Bars
Numerical Results
Current State of Art
Conclusions
References
Challenges in the Simulation of Radio Frequency Circuits
Introduction
Network equations
Simulation of Radio Frequency Circuits
The Embedding Technique
References
An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics
Introduction
From digital twin to real-time analysis
Advanced geometrical parametrization with automatic CAD files interface
Parameter space dimensionality reduction
Data driven model order reduction
Dynamic mode decomposition
Proper orthogonal decomposition with interpolation
Simulation-based design optimization framework
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
Historical background
Stability of Kelvin’s gyrostat and spinning artillery shells filled with liquid
Secular instability of the Maclaurin spheroids by viscous and radiative losses
Brouwer’s rotating vessel
Stability and instability without friction
Stability of triangular libration points L and L
Destabilization by friction
Indefinite damping and PT-symmetry
Ziegler’s paradox
Bottema’s analysis of Ziegler’s paradox
An umbrella without dynamics
Hopf bifurcation near : resonance and structural stability
Abscissa minimization, robust stability and heavy damping
Abscissa minimization and multiple roots
Swallowtail singularity as the global minimizer of the abscissa
References
Data Analysis and finance
Topological Data Analysis
Introduction
About this paper
The need of new mathematical and algorithmic tools
The emergence of geometric inference and persistent homology
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
Persistent homology
Persistent homology for machine learning
The algorithmic and software challenges of TDA
New research directions
Conclusion
A brief glossary
References
Prediction Models with Functional Data for Variables related with Energy Production
Introduction
Functional Data Models
Application to Iberian Market Energy
Variable selection
The selection algorithm
Numerical results
Real data application
Energy Market Demand
Energy Price
Conclusions
References
Quantization Methods for Stochastic Differential Equations
Introduction
Finance and Stochastic Differential Equations
Quantization
Outline of the Paper
Vector Quantization
Optimal Quantization Grids
Numerical Methods
Lloyd’s Algorithm
The Newton-Raphson Algorithm
Recursive Marginal Quantization
Numerical Methods
The Zero Boundary
Higher-order Updates
Recursive Marginal Quantization for Stochastic Volatility Models
Numerical Results
Numerical Convergence Results
An Example of a Local Volatility Model
Stochastic Volatility Models
Calibration
Conclusion
References
Index

Gunther M. Novel Mathematics Inspired by Industrial Challenges 2022.pdf12.01 MiB