Force-Gradient Nested Multirate Methods for Hamiltonian System

2013/12/11 by Dmitry Shcherbakov, Matthias J. Ehrhardt, Shcherbakov, Dmitry +5
Engineering · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nuclear reactor physics and engineering #Numerical Analysis (math.NA) #Numerical methods for differential equations #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1312.3113

openalex publication_date 2013/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Force-gradient decomposition methods are used to improve the energy preservation of symplectic schemes applied to Hamiltonian systems. If the potential is composed of different parts with strongly varying dynamics, this multirate potential can be exploited by coupling force-gradient decomposition methods with splitting techniques for multi-time scale problems to further increase the accuracy of the scheme and reduce the computational costs. In this paper, we derive novel force-gradient nested methods and test them numerically. Such methods can be used to increase the acceptance rate for the molecular dynamics step of the Hybrid Monte Carlo algorithm (HMC) and hence improve its computational efficiency.

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