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Reduced order multirate schemes for coupled systems / vorgelegt von Marcus W.F.M. Bannenberg. Wuppertal, 2022
Inhalt
Introduction
1 Differential-Algebraic Equations
1.1 Basic Definitions
1.2 Problems in Implicit Form
2 Integrated Circuit Simulation
2.1 Modified Nodal Analysis
2.1.1 Charge-Oriented MNA
2.1.2 Extension of Basic MNA
2.2 Transient Analysis
3 Model Order Reduction
3.1 Reduction by Galerkin Projection
3.1.1 Proper Orthogonal Decomposition
3.1.2 Maximum Entropy Snapshot Sampling
3.1.3 POD Compared With MESS
3.2 Hyper-Reduction
3.2.1 Discrete Empirical Interpolation Method
3.2.2 Gappy Reconstruction
3.2.3 Hyper-Reduction Comparison
3.3 DAE Reduction
3.3.1 Gauß-Newton with Approximated Tensors
4 Numerical Integration Methods
4.1 Index-1 Problems
4.1.1 Runge Kutta Methods
4.1.2 Backward Differentiation Formula
4.2 Multirate Integration
4.2.1 Partitioning
4.2.2 Different Multirate Approaches
4.3 Reduced Order Multirate
4.3.1 DAE-ODE Coupling
4.3.2 DAE-DAE Coupling
4.4 Numerical Analysis
4.4.1 DAE-ODE Coupling
4.4.2 DAE-DAE Coupling
5 Applications
5.1 Academic Experiments
5.1.1 The Diode Chain Model
5.1.2 System of Coupled DAEs
5.2 Industrial Applications
5.2.1 The Thermal-Electric Circuit
5.2.2 Solar Panel Simulation
Conclusions and Outlook
References