Multilevel algorithms in Lattice QCD for exascale machines / eingereicht von Gustavo Alsonso Ramírez Hidalgo, M.Sc. Wuppertal, 14. July 2022
Inhalt
- Acknowledgments
- Foreword
- Contents
- Introduction
- Quantum chromodynamics on the lattice
- The standard model and quantum chromodynamics
- Path integral and hybrid Monte Carlo
- Lattice discretizations in quantum chromodynamics
- Disconnected diagrams
- Other theories: the Schwinger model
- Domain decomposition aggregation-based αdaptive algebraic multigrid method
- Numerical linear algebra fundamentals
- Eigenvalues, singular values and conditioning
- Iterative methods for sparse linear systems of equations
- Multigrid methods
- Algebraic multigrid
- Coarsest level improvements
- Krylov based improvements
- Numerical tests: Krylov based
- LU based improvements
- Numerical tests: LU based
- Outlook on coarsets-level computations
- Hybrid GPU/CPU DD-αAMG
- Multigrid Multilevel Monte Carlo
- Stochastic trace estimation and multilevel Monte Carlo
- Multilevel Monte-Carlo
- Stochastic estimation of the trace of a matrix
- Multilevel Monte-Carlo for the trace of the inverse
- Numerical tests
- Outlook on multigrid multilevel Monte Carlo
- List of Figures
- List of Tables
- List of Algorithms & Scripts
- Bibliography