Hachtel, Christoph Johannes: Multirate time integration methods for efficient time domain simulation of large-scale systems and differential-algebraic equations. Wuppertal, 7. September 2020
Content
- Contents
- Abbreviations
- List of symbols
- 1 Introduction
- 2 Preliminaries
- 3 Multirate Time Integration for Order Reduced Systems
- 3.1 Model Order Reduction for Linear Time Invariant Systems
- 3.1.1 Projection-Based Model Order Reduction
- 3.1.2 Balanced Truncation Model Order Reduction
- 3.1.3 Model Order Reduction for Coupled LTI-systems
- 3.1.4 The Logarithmic Matrix Norm
- 3.2 Model Order Reduction for Multiscale Ordinary Differential Equations
- 3.2.1 Multirate Linear Implicit Methods
- 3.2.2 Multirate Time Integration for Order Reduced Subsystems
- 3.2.3 Interface Reduction
- 3.2.4 Simulation of an Electric-Thermal Problem with Reduced Interface
- 3.3 An Error Estimate for the Multirate-MOR -Method
- 3.3.1 Problem Setting
- 3.3.2 Error Definition and Splitting
- 3.3.3 A Time-Domain Error Bound for EMOR
- 3.3.4 An Error Recursion for EMR for Balanced Systems
- 3.4 Multirate Time Integration and MOR for a Field-Circuit Coupled System
- 4 Multirate One-Step Methods for Differential-Algebraic Equations
- 4.1 An Introduction to Differential-Algebraic Equations
- 4.1.1 Differential-Algebraic Equations – Definition and Index Concept
- 4.1.2 One-Step Methods for semi-explicit DAEs of index-1
- 4.2 The Multirate Implicit Euler Method for Semi-Explicit DAEs of Index-1
- 4.2.1 Multiscale Differential-Algebraic Equations
- 4.2.2 The mrIRK-1 Scheme for Semi-Explicit DAEs of Index-1
- 4.2.3 Consistency Analysis for mrIRK1-DAE
- 4.2.4 Convergence of mrIRK1-DAE
- 4.2.5 Numerical Results
- 4.3 A Second Order Multirate Runge-Kutta Method for DAEs
- 4.3.1 The mrIRK2-DAE Scheme based on LobattoIIIC
- 4.3.2 Consistency Analysis for mrIRK2-DAE
- 4.3.3 Convergence of mrIRK2-DAE
- 4.3.4 Numerical Results
- 4.4 Decoupled Multirate One-Step Methods – A Link to Dynamic Iteration
- 5 Summary
- A Convergence Plots of the mrIRK1-DAE scheme
- References