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Parallel and explicit time integration of transient nonlinear magneto- and electroquasistatic fields / von Jennifer Susanne Dutiné, M. Sc. Wuppertal, 08.04.2020
Content
List of Figures
List of Tables
List of Algorithms
List of Abbreviations
List of Symbols
Introduction
Previous and Related Works
Overview
Mathematical Description of Electromagnetic Field Problems
Maxwell's Equations
The Magnetoquasistatic and Electroquasistatic Approximation
Discretization of Partial Differential Equations in Space and Time
The Finite Element Method
FEM applied to the PDE of Magnetoquasistatic Field Problems
FEM Applied to the PDE of Electroquasistatic Field Problems
Time Integration Methods
The Implicit Euler Method
The Explicit Euler Method
Solving Large Systems of Algebraic Equations
The Conjugate Gradient Method
The Sparse LU-Decomposition
(Semi-) Explicit Time Integration of the Magnetoquasistatic Field Problem
Application of the Moore-Penrose Pseudo-Inverse
Numerical Validation: Application of a Pseudo-Inverse
Results for the TEAM 7 benchmark problem
Results for the TEAM 10 benchmark problem
Improved Start Vector Generation Within Semi-Explicit Time Stepping
Subspace Projection Extrapolation and Cascaded Subspace Projection Extrapolation
Proper Orthogonal Decomposition for MRHS Problems
Numerical Validation: Improved Start Vectors
Selective Matrix Update Bypass Strategy
Numerical Validation of the Selective Matrix Update Bypass Strategy
GPU-Accelerated Inverse Computations
Numerical Validation
Parallel-In-Time Integration of Transient Electroquasistatic Field Problems Using Parareal
Mathematical Formulation
Numerical Validation
Results of Simulations with a Linear Field Grading Material
Results of Simulations with a Nonlinear Field Grading Material
Conclusion and Outlook
Bibliography
Publications by the Author