University of Twente Student Theses


Structure-preserving integrators for Molecular Dynamics

Goor, L.A. van (2023) Structure-preserving integrators for Molecular Dynamics.

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Abstract:Fast and accurate time integrators for Molecular Dynamics (MD) simulations are needed to investigate the properties of materials without the experimental costs. This thesis illustrates the implementation and benefits of a structure-preserving time-integration method for structured MD models. We compare the Trapezoidal Munthe-Kaas (TMK) method, a Lie group integrator, with the widely used Verlet method for MD simulations. The Verlet method fails to conserve additional symmetry present in model simulations, leading to the development of asymmetry and inaccurate particle trajectories. In contrast, the TMK method, implemented with Flaschka variables, conserves additional symmetry of model simulations and exhibits qualitatively different behavior compared to the Verlet method. Preserving the structure and conserving the constants of motion in the governing equations through MD simulations can provide significant advantages. We demonstrate the effectiveness of the TMK method through multiple small and generic MD models that feature different potential forces, including the Lennard-Jones potential. Our approach could easily be extended to real MD simulations, which indicates the promising application of the TMK method for MD.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
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