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