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Parallel-in-Time integration with application to eddy current simulations / eingereicht von Jens Hahne, M.Sc. Wuppertal, 25.04.2023
Content
Acknowledgments
Foreword
Contents
Introduction
Review of basic material
Differential equations
Ordinary differential equations
Differential-algebraic equations
Partial differential equations
Discretization
Spatial discretization
Temporal discretization
Solvers
Iterative methods
Newton method
Governing application
The Maxwell equations
Magnetoquasistatic approximation
Electric circuit theory
PWM signals
Induction motors
Parallel-in-time integration
Parareal
PFASST
MGRIT
Two-level MGRIT
Multilevel FAS MGRIT
Error propagation
Convergence bounds
AT-MGRIT
Two-level AT-MGRIT
Multilevel FAS AT-MGRIT
Error propagation
Convergence bounds
Convergence criterion
Implementation
PyMGRIT
Numerical experiments: AT-MGRIT investigations
Heat equation
Gray-Scott problem
Discussion of spatial parallelism
Numerical experiments: Induction machine
Numerical model
PWM voltage source
Linear material model
Nonlinear material model
Sinusoidal voltage source
AT-MGRIT
PinT optimization
Performance Model
Performance analysis
Creating task graphs from PinT algorithms
Adoption of typical PinT scheduling
Discussion about appropriate weighting of task
Results
PFASST
MGRIT
Conclusions & Outlook
List of Figures
List of Tables
List of Notations
Bibliography