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Automated local Fourier analysis (aLFA) and geometric multigrid for graphene / eingereicht von Nils Kintscher. Wuppertal, 29. Juli 2019
Inhalt
Introduction
Normal forms of integer matrices
The Hermite normal form
The Smith normal form
Crystalline structures
Lattices
Primitive cells
Crystals
Quotient spaces
The dual lattice
Operators on lattices and crystals
Function spaces
Operators
Automated Local Fourier Analysis (aLFA)
Linear iterative methods
Convergence theory
Splitting methods
Multigrid methods
Symmetries in colored smoothers
Smoothing analysis
Graphene
Crystal structure of graphene
Tight-binding Hamiltonian
Components of the geometric multigrid method
Analysis of the coarse grid correction
Convergence rates of the multigrid method
Open boundaries
Conclusion
Algorithms
Nomenclature