Condensed Matter Physics, 2002, vol. 5, No. 3(31), p. 369-390, English

Author(s): I.P.Omelyan, I.M.Mryglod (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine; Institute for Theoretical Physics, University of Linz, A-4040 Linz, Austria), R.Folk (Institute for Theoretical Physics, University of Linz, A-4040 Linz, Austria)

The method of molecular dynamics (MD) is a powerful tool for the prediction and investigation of various phenomena in physics, chemistry and biology. The development of efficient MD algorithms for integration of the equations of motion in classical and quantum many-body systems should therefore impact a lot of fields of fundamental research. In the present study it is shown that most of the existing MD integrators are far from being ideal and further significant improvement in the efficiency of the calculations can be reached. As a result, we propose new optimized algorithms which allow to reduce the numerical uncertainties to a minimum with the same overall computational costs. The optimization is performed within the well recognized decomposition approach and concerns the widely used symplectic Verlet-, Forest-Ruth-, Suzuki- as well as force-gradient-based schemes. It is concluded that the efficiency of the new algorithms can be achieved better with respect to the original integrators in factors from 3 to 1000 for orders from 2 to 12. This conclusion is confirmed in our MD simulations of a Lennard-Jones fluid for a particular case of second- and fourth-order integration schemes.

Key words: molecular dynamics, symplectic integration, decomposition method, splitting method, order conditions, numerical schemes
PACS: 02.60.Cb, 02.70.Ns, 05.10.-a, 95.10.Ce, 95.75.Pq

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