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Multilevel algorithms in Lattice QCD for exascale machines / eingereicht von Gustavo Alsonso Ramírez Hidalgo, M.Sc. Wuppertal, 14. July 2022
Content
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
Motivation
Two levels and multilevel multigrid
Algebraic multigrid
Algebraic multigrid in lattice QCD
Aggregation-based prolongation and restriction
Petrov-Galerkin approach
Domain decomposition aggregation-based αdaptive algebraic multigrid method
DD-αAMG for twisted mass fermions
Coarsest level improvements
Krylov based improvements
Numerical tests: Krylov based
The clover-improved Wilson operator
The twisted mass operator
LU based improvements
Direct solves via MUMPS
Numerical tests: LU based
Outlook on coarsets-level computations
Hybrid GPU/CPU DD-αAMG
SAP in DD-αAMG
Schwarz Alternating Procedure on GPUs
Domain Decomposition: GPUs vs CPUs
SAP in DD-αAMG on GPUs: implementation details
Numerical tests
SAP on GPUs
Hybrid GPU+CPU DD-αAMG solver
Outlook on GPU implementations
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
Schwinger model
LQCD I: clover-improved Wilson-Dirac operator
LQCD II: twisted mass operator
Outlook on multigrid multilevel Monte Carlo
List of Figures
List of Tables
List of Algorithms & Scripts
Bibliography