Khalil, Mostafa Nasr: Multigrid multilevel Monte Carlo approaches for trace estimation in lattice QCD. Wuppertal, Monday 19th June, 2023
Content
- Acknowledgments
- Abstract
- Foreword
- Contents
- Introduction
- Mathematical definitions
- Quantum chromodynamics on the Lattice
- Linear Solvers
- Stochastic Trace Estimation
- Variance Reduction Methods
- Multigrid Multilevel Monte Carlo
- Standard Monte Carlo method
- Multilevel Monte Carlo
- Two-level MC
- Multilevel Monte Carlo (MLMC) theory
- Multilevel Monte Carlo for trace estimation
- Error bounds of multilevel Monte Carlo methods
- Multigrid Multilevel Monte Carlo Method
- Stopping criteria in Multigrid Multilevel Monte Carlo
- Numerical Results
- Methodology
- Two-dimensional Laplace
- Gauge Laplace
- Schwinger Model
- Lattice QCD
- Conclusion and Outlook
- List of Figures
- List of Tables
- Bibliography