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Multiscale modeling and multirate time integration of field, circuit coupled problems / von Sebastian Schöps. 2011
Inhalt
List of Figures
List of Symbols
Introduction
Multiscale and Multirate
Related Works
Overview
Electromagnetism
Maxwell's Equations
Boundary and Initial Conditions
Partitioning into Regions and Materials
Space Discretization
Maxwell's Grid Equations
Semi-discrete Problem Formulation
Gauging
Conclusions
Multiscale Device Models
Electric Network
Magnetoquasistatic Conductor Model
More Conductor Models
Semiconductor Device Model
Conclusions
DAE-Index Analysis
Tractability Index
Index Analysis for the Field/Circuit Problem
Index-1 Conditions
Index-2 Conditions
Conclusions
Multirate Methods
Single Rate DAE Time-integration
Multirate Bypassing of MQS Schur Complements
Bypassing as Multirate Time-Integration
Conclusions
Multirate Cosimulation
Abstract DAE-DAE Coupling
Dynamic Iteration
Recursion Estimate
Convergence and Stability
Application to Field/Circuit Coupling
Application to Semiconductor/Circuit Coupling
Domain Substructuring in MQS Devices
Linear/Nonlinear Decomposition
Convergence and Eigenvalues
Inner Solvers
Conclusions
Numerical Examples
DAE-Index in Applications
Multirate Bypassing
Conclusion
Cosimulation
Field/Circuit Problem
Semiconductor/Circuit Problem
Domain Substructuring of a Transformer
2D Test Problem
3D Test Problem
Conclusions
Conclusions
Outlook
Discretization Properties
Discrete Operators
FIT Numbering Scheme
Phantom Objects on Finite Grids
Degrees of Freedom in FIT
Material Matrices
Element Matrices
Global Matrix Assembly
Nonlinearity
Differential Curl-Curl Matrix
Bibliography