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2021 | Buch

Mathematical Analysis and Simulation of Field Models in Accelerator Circuits

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Über dieses Buch

This book deals with the analysis and development of numerical methods for the time-domain analysis of multiphysical effects in superconducting circuits of particle accelerator magnets. An important challenge is the simulation of “quenching”, i.e. the transition of a material from the superconducting to the normally electrically conductive state. The book analyses complex mathematical structures and presents models to simulate such quenching events in the context of generalized circuit elements. Furthermore, it proposes efficient parallelized algorithms with guaranteed convergence properties for the simulation of multiphysical problems. Spanning from theoretical concepts to applied research, and featuring rigorous mathematical presentations on one side, as well as simplified explanations of many complex issues, on the other side, this book provides graduate students and researchers with a comprehensive introduction on the state of the art and a source of inspiration for future research. Moreover, the proposed concepts and methods can be extended to the simulation of multiphysical phenomena in different application contexts.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
This chapter gives the motivation behind the analysis and simulation methods presented in this thesis and introduces the previous work performed in related topics.
Idoia Cortes Garcia
Chapter 2. Modelling
Abstract
The different physical phenomena that are relevant through this work are described by either space and time dependent partial differential equations or only time dependent differential algebraic equations. This chapter presents the different systems of equations that are required in this work, as well as the quantities that are involved. This includes the partial differential equations required for the description of electromagnetic fields, i.e. Maxwell’s equations and their different approximations, as well as the heat propagation. Furthermore, the system of differential equations for circuit simulation (modified nodal analysis) is derived and introduced.
Idoia Cortes Garcia
Chapter 3. Numerical Methods and Model Analysis
Abstract
For real world application set-ups, a closed-form solution of the systems of equations that model the physical phenomena is rare. Therefore, numerical methods are used that yield an approximation of the solution. The systems of differential equations presented in the previous section are both space-dependent boundary value problems as well as time-dependent initial value problems. To approximate the solution of these two types of problems, different numerical techniques are used. This chapter deals with the theoretical fundamentals of both space as well as time integration methods and with important concepts concerning the analysis of the systems of equations.
Idoia Cortes Garcia
Chapter 4. Structural Analysis of the Coupled Systems
Abstract
The time dependent systems of equations obtained in most simulation settings of this work are systems of differential algebraic equations. These systems can be classified according to their index. Systems with higher index require special numerical treatment. Therefore, when dealing with (coupled) systems of differential algebraic equations, a priori knowledge about their index allows to properly handle their simulation. This chapter presents three generalised elements definitions as well as the index analysis of the system of equations arising from circuits (modified nodal analysis) containing the generalised elements. For each one of the definitions, examples arising from different approximations of Maxwell’s equations are given.
Idoia Cortes Garcia
Chapter 5. Iterative Methods in Time Domain
Abstract
The simulation of large, coupled, multiphysical problems typically poses considerable challenges. Their multiphysical character frequently involves the coupling of systems of equations with different mathematical properties, time rates and sizes, whose coupled solution has to be numerically approximated together with one method. Furthermore, especially when considering space-discretised models, each subsystems can become very large and computationally costly to solve. In this chapter two time domain simulation algorithms are presented that can be applied to field-circuit coupled systems. This includes co-simulation techniques (in particular the waveform relaxation method) that can be used to exploit the different mathematical properties of the systems. Also, to further speed up the computation time, the parallel-in-time method Parareal is presented and adapted to the case of differential-algebraic equations.
Idoia Cortes Garcia
Chapter 6. Results
Abstract
In this chapter the theoretical results presented in the previous chapters are verified by means of numerical test examples. Furthermore a summary of the whole work and an outlook to future work is given.
Idoia Cortes Garcia
Backmatter
Metadaten
Titel
Mathematical Analysis and Simulation of Field Models in Accelerator Circuits
verfasst von
Dr. Idoia Cortes Garcia
Copyright-Jahr
2021
Electronic ISBN
978-3-030-63273-1
Print ISBN
978-3-030-63272-4
DOI
https://doi.org/10.1007/978-3-030-63273-1

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