Numerical integrators for the Hybrid Monte Carlo method
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València（瓦伦西亚理工大学多学科数学研究所）；Institut de Matemàtiques i Aplicacions de Castelló and Departament de Matemàtiques, Universitat Jaume I（卡斯特利翁数学与应用研究所及瓦莱西亚大学数学系）；Departamento de Matemática Aplicada e IMUVA, Facultad de Ciencias, Universidad de Valladolid（巴利亚多利德大学理学院应用数学系及IMUVA）
Sergio Blanes, Fernando Casas, J. M. Sanz-Serna
备注：
30 pages, 5 figures
发表信息：
SIAM J. Sci. Comput. 36, No. 4 (2014), A1556-A1580
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy of the integrator and/or reducing the size of its error constants; order and error constant are relevant concepts in the limit of vanishing step-length. We propose an alternative methodology based on the performance of the integrator when sampling from Gaussian distributions with not necessarily small step-lengths. We construct new splitting formulae that require two, three or four force evaluations per time-step. Limited, proof-of-concept numerical experiments suggest that the new integrators may provide an improvement on the efficiency of the standard Verlet method, especially in problems with high dimensionality.
Adaptive multi-stage integrators for optimal energy conservation in molecular simulations
BCAM - Basque Center for Applied Mathematics（巴斯克应用数学中心）；IKERBASQUE, Basque Foundation for Science（伊卡萨克斯克，巴斯克科学基金会）；Departamento de Matemáticas, Universidad Carlos III de Madrid（马德里卡洛斯三世大学数学系）
