Project Details
Projekt
Monte Carlo sampling of gluons by molecular dynamics
Applicant
Professor Dr. Michael Günther
Subject Area
Mathematics
Term
since 2021
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 451886959
The main goal of this project is to develop new techniques to improve the sampling of gauge fields including quark effects based on the HMC algorithm by a) constructing schemes based on the Cayley transform and b) generalizing this approach with respect to multirate schemes for exploiting different strength of forces and allowing for including constraints. We will develop symplectic numerical time integration schemes for Monte-Carlo samplings of lattice QCD, which are based on the Cayley transform instead of the exponential mapping. Hereby we will proceed in two ways: on the one hand, we will transform current state-of-art schemes to the Cayley mapping approach, and implement adapted nested integration schemes into the openQCD code; on the other hand, as an alternative approach, we will generalize symplectic GARK schemes from the Abelian setting to the non-Abelian setting. The Cayley transform setting will be applied to optimize the gauge link smearing used in projects 1 and 2 and for constructing higher-order symmetric schemes to compute the small gauge updates in project 2.We will generalize the Cayley transform based time integration schemes in two ways: a) symplectic schemes will exploit the different dynamics given in different partitions of the Hamiltonian according to the strength of forces, with an emphasis on force-gradient and GARK schemes; b) we will derive symmetric multirate GARK schemes for computing small gauge updates. In addition, we will generalize multirate GARK schemes to a DAE setting on the one hand, and construct trivializing maps for optimally exploiting multirate potential.To provide all algorithms derived in this project to the lattice community, we will implement them in the open-source (GPL v2) package openQCD.
DFG Programme
Research Units
